Prediction of out of specification based on a spatial characteristic of process variability

ABSTRACT

A method for determining a probabilistic model configured to predict a characteristic (e.g., defects, CD, etc.) of a pattern of a substrate subjected to a patterning process. The method includes obtaining a spatial map of a distribution of a residue corresponding to a characteristic of the pattern on the substrate, determining a zone of the spatial map based on a variation of the distribution of the residue within the spatial map, and determining the probabilistic model based on the zone and the distribution of the residue values or the values of the characteristic of the pattern on the substrate within the zone.

This application claims the benefit of priority of U.S. patentapplication No. 62/757,397, which was filed on Nov. 8, 2018, and whichis incorporated herein in its entirety by reference.

TECHNICAL FIELD

The description herein relates generally to a method to predict physicalitems that are out of specification, such as out of specificationpattern instances on a substrate produced by a device manufacturingprocess.

BACKGROUND

A lithography apparatus is a machine that applies a desired pattern ontoa target portion of a substrate. Lithography apparatus can be used, forexample, in the manufacture of integrated circuits (ICs). In thatcircumstance, a patterning device, which is alternatively referred to asa mask or a reticle, may be used to generate a circuit patterncorresponding to an individual layer of the IC, and this pattern can beimaged onto a target portion (e.g. comprising part of, one or severaldies) on a substrate (e.g. a silicon wafer) that has a layer ofradiation-sensitive material (resist). In general, a single substratewill contain a network of adjacent target portions that are successivelyexposed. Known lithography apparatus include so-called steppers, inwhich each target portion is irradiated by exposing an entire patternonto the target portion in one go, and so-called scanners, in which eachtarget portion is irradiated by scanning the pattern through the beam ina given direction (the “scanning”-direction) while synchronouslyscanning the substrate parallel or anti parallel to this direction.

Prior to transferring the circuit pattern from the patterning device tothe substrate, the substrate may undergo various procedures, such aspriming, resist coating and a soft bake. After exposure, the substratemay be subjected to other procedures, such as a post-exposure bake(PEB), development, a hard bake and measurement/inspection of thetransferred circuit pattern. This array of procedures is used as a basisto make an individual layer of a device, e.g., an IC. The substrate maythen undergo various processes such as etching, ion-implantation(doping), metallization, oxidation, chemo-mechanical polishing, etc.,all intended to finish off the individual layer of the device. Ifseveral layers are required in the device, then the whole procedure, ora variant thereof, is repeated for each layer. Eventually, a device willbe present in each target portion on the substrate. These devices arethen separated from one another by a technique such as dicing or sawing,whence the individual devices can be mounted on a carrier, connected topins, etc.

Thus, manufacturing devices, such as semiconductor devices, typicallyinvolves processing a substrate (e.g., a semiconductor wafer) using anumber of fabrication processes to form various features and multiplelayers of the devices. Such layers and features are typicallymanufactured and processed using, e.g., deposition, lithography, etch,chemical-mechanical polishing, and ion implantation. Multiple devicesmay be fabricated on a plurality of dies on a substrate and thenseparated into individual devices. This device manufacturing process maybe considered a patterning process. A patterning process involves apatterning step, such as optical or nanoimprint lithography using apatterning device in a lithographic apparatus, to transfer a pattern onthe patterning device to a substrate and typically, but optionally,involves one or more related pattern processing steps, such as resistdevelopment by a development apparatus, baking of the substrate using abake tool, etching using the pattern using an etch apparatus, etc.

SUMMARY

Whether physical items of a physical system or object (e.g., patternfeatures on a substrate) are out of specification (e.g., defects) is asignificant consideration in, for example, control, modification,design, etc. of a physical item or object or a process involving thephysical item or object. Accordingly, there is desired a technique thatenables improved prediction of out of specification physical items for,e.g., an improved measurement sampling plan for taking measurements ofthe physical items (e.g., pattern instances on a substrate produced by adevice manufacturing process).

According to an embodiment, there is provided a method for determining aprobabilistic model configured to predict a characteristic of a patternon a substrate subjected to a patterning process. The method includesobtaining a spatial map of a distribution of a residue corresponding toa characteristic of the pattern on the substrate; determining, via acomputing system, a zone of the spatial map based on a variation of thedistribution of the residue within the spatial map; and determining, viathe computing system, the probabilistic model based on the zone and thedistribution of the residue values or the values of the characteristicof the pattern on the substrate within the zone.

In an embodiment, the determining the zone includes determining whetherthe variation of the distribution of the residue exceeds a predefinedthreshold; and responsive to the exceeding of the predefined threshold,defining a different zone.

In an embodiment, the determining the zone is an iterative process,wherein a plurality of zones are obtained based on the variation of thedistribution of the residue, such that a first zone of the plurality ofzones has a first variation of the distribution of the residue, and asecond zone of the plurality of zones has a second variation of thedistribution of the residue.

In an embodiment, an iteration of the determining the zone includesexecuting a classification algorithm with the spatial map of thedistribution of the residue as input, the classification algorithmproviding one or more groups of the residue based on the variation inresidue; and identifying a boundary around each group of the one or moregroups of residue, wherein the zone is a region within the boundary.

In an embodiment, the iteration of the determining the zone furtherincludes obtaining, via a metrology tool, metrology data in the firstzone and the second zone corresponding to the characteristic of thepattern on the substrate, wherein the first zone and the second zone areseparated by a first boundary between the first zone and the secondzone, and the second zone is identified by a second boundary; andmodifying the first boundary around the first zone of the residue basedon the metrology data.

In an embodiment, the classification algorithm is a machine learningmodel trained to identify zones based on the variation of thedistribution of the residue or the variation of the characteristic ofthe pattern on the substrate.

In an embodiment, the classification algorithm involves a clusteringanalysis based on at least one of: k-nearest mean; mean-shifting;naive-Bayes and back propagation neural network; Density-Based SpatialClustering of Applications with Noise; Gaussian mixture model; orhierarchical clustering.

In an embodiment, the determining the zone includes determining a radialboundary and an angular span of the radial boundary based on thevariation of the distribution of the residue exceeding a predefinedthreshold in the radial direction, an angular direction or a combinationthereof.

In an embodiment, the zone is defined in terms of radial distance from acenter of the substrate.

In an embodiment, the zone comprises an irregular closed boundary in aradial direction and spanning a certain angular region of the substrate.

In an embodiment, the determining the probabilistic model includesobtaining values of the characteristic of the pattern on the substratewithin the zone; and determining statistical parameters of theprobabilistic model based on values of the characteristic of the patternor values of the residue corresponding to the characteristic of thepattern within the zone.

In an embodiment, the statistical parameters of the probabilistic modelcomprise a mean and standard deviation values.

In an embodiment, the probabilistic model is a Gaussian distribution.

In an embodiment, the method further includes obtaining, via a metrologytool, additional metrology data corresponding to subsequently processedsubstrates and distribution of the residues corresponding to theadditional data; adjusting, via the computing system, the zone based onthe distribution of the residues corresponding to the additional data;and adjusting, via the computing system, the probabilistic model basedon the adjusted zone.

In an embodiment, the adjusting of the probabilistic model comprisesadjusting a statistical parameter of the probabilistic model to improveaccuracy of measurements.

In an embodiment, the method further includes ordering, via thecomputing system, the plurality of zones from a highest value to alowest value of the variation of the distribution of the residue withinthe spatial map; and guiding, via the computing system, the metrologytool to measure a characteristic of a pattern at different locations ona substrate based on the ordered plurality of zones.

In an embodiment, the method further includes determining, via thecomputing system, the characteristics of the pattern on the substratethat are outside a specification based on the measurements from themetrology tool.

In an embodiment, wherein the characteristic is one or more selectedfrom: a position relative to a substrate, a position relative to one ormore other physical item instances, a geometric size, a geometric shape,a measure of a stochastic effect, and/or any combination selectedtherefrom.

In an embodiment, the method further includes determining, via thecomputing system, an attribute of the distribution of the residue basedon simulation data and measured data corresponding to the characteristicof an ensemble of physical items.

In an embodiment, the attribute of the distribution of the residue withrespect to the ensemble of physical items comprises a cumulativedistribution function for the ensemble of physical item instances.

In an embodiment, the physical item instance corresponds to a patterninstance on a substrate produced by a device manufacturing process.

In an embodiment, the method further includes determining, based on theprobability determined by probabilistic model, or the adjustedprobabilistic model, the predicted presence of at least one physicalitem instance out of specification in a measurement location or field ofview of a metrology tool.

In an embodiment, further includes determining, based on the probabilitydetermined by probabilistic model, or the adjusted probabilistic model,a sampling plan comprising measurement locations on a substrate formeasurements of a characteristic to determine physical item instances,if any, that are out of specification.

Furthermore, according to an embodiment, there is provided a method fordetermining, for a metrology tool, a sampling plan of a patterningprocess. The method includes obtaining a probabilistic modelcorresponding to a zone of a substrate; predicting, via a computingsystem, a probability using the probabilistic model; and determining,via the computing system, based on the probability, a sampling plancomprising measurement locations on the substrate for measurements of acharacteristic to determine whether the substrate is out ofspecification.

In an embodiment, the method further includes obtaining a spatial map ofa distribution of a residue corresponding to a characteristic of apattern on the substrate; obtaining a plurality of zones of thesubstrate based on the distribution of the residue and based on aprobabilistic model per zone of the plurality of zones; and ordering,via the computing system, the plurality of zones such that a zone of theplurality of zones is arranged a descending order based on associatedvalues of the variation of the distribution of the residue within thespatial map, where the determining of the sampling plan is based on theordering of the plurality of zones and the probability predicted by theprobabilistic model corresponding to a given zone.

In an embodiment, the method further includes guiding, based on thesampling plan, the metrology tool to measure a characteristic of apattern at different locations on the substrate produced by thepatterning process.

In an embodiment, the determining the sampling plan includes obtaining,via the metrology tool, additional metrology data corresponding tosubsequently processed substrates and distribution of the residuescorresponding to the additional data; adjusting, via the computingsystem, a given zone of the plurality of zones based on the distributionof the residues corresponding to the additional data; adjusting, via thecomputing system, the probabilistic model based on the adjusted zone;and adjusting, via the computing system, the sampling plan based on theprobability determined by the adjusted probabilistic model.

In an embodiment, the adjusting of the probabilistic model comprisesadjusting a statistical parameter of the probabilistic model to improveaccuracy of measurements.

Furthermore, according to an embodiment, there is provided a method fordetermining zones of a substrate based on process variability of apatterning process. The method includes obtaining (i) a spatial map of adistribution of a residue corresponding to a characteristic of a patternon a substrate, and (ii) a process variation of a parameter of thepatterning process; detecting, via a computing system, a relationshipbetween the spatial map of the distribution of the residue and theprocess variation of the parameter of the patterning process;determining, via the computing system, a zone based on the relationship;and determining, via the computing system, the probabilistic model basedon the zone and the distribution of the residue values or the values ofthe characteristic of the pattern on the substrate within the zone.

In an embodiment, the determining the zone includes determining, basedon the relationship, whether the process variation of the parameter ofthe patterning process causes a change in the distribution of theresidue to exceed a predefined threshold; and responsive to theexceeding of the predefined threshold, defining a different zone.

In an embodiment, the parameter of the patterning process is at leastone of dose, focus, an optical parameter, or moving standard deviationof movement of the substrate.

Furthermore, according to an embodiment, there is provided a computerprogram product comprising a non-transitory computer readable mediumhaving instructions recorded thereon, the instructions when executed bya computer system implementing the methods above.

BRIEF DESCRIPTION OF THE DRAWINGS

The above aspects and other aspects and features will become apparent tothose ordinarily skilled in the art upon review of the followingdescription of specific embodiments in conjunction with the accompanyingfigures, wherein:

FIG. 1 schematically depicts a lithography apparatus according to anembodiment.

FIG. 2 schematically depicts an embodiment of a lithographic cell orcluster according to an embodiment.

FIG. 3 schematically depicts a method of predicting defects in a devicemanufacturing process according to an embodiment.

FIG. 4 illustrates a flowchart for a method of simulating at least aportion of a pattern or a characteristic of a pattern in an imageaccording to an embodiment.

FIG. 5 is a flow chart of a method for determining a probabilistic modelconfigured to predict a characteristic of a patterning process accordingto an embodiment.

FIG. 6A is an example distribution of a residual according to anembodiment.

FIG. 6B is an example probability of defect based on the distribution ofthe residue in FIG. 6A according to an embodiment.

FIG. 6C is an example spatial map according to an embodiment.

FIG. 6D is an example sampling based on the spatial map of FIG. 6Caccording to an embodiment.

FIG. 7 illustrates an example method of obtaining a spatial map of thedistribution of a residue according to an embodiment.

FIG. 8A illustrates example values standard deviation of a distributionof a residue on a substrate in a radial direction according to anembodiment.

FIG. 8B is an example histogram of the distribution of the residuewithin a region spanning a particular radial distance according to anembodiment.

FIG. 8C is an example histogram of a distribution of residue at the edgeregion of the substrate according to an embodiment.

FIG. 9 illustrates example zones determined based on a distribution ofthe residue according to an embodiment.

FIG. 10 is a flow chart of a method for determining a sampling plan fora metrology tool of a patterning process according to an embodiment.

FIG. 11 is a flow chart of a method for determining zones of a substratebased on a process variability of a patterning process according to anembodiment.

FIG. 12 schematically depicts an embodiment of a scanning electronmicroscope (SEM) according to an embodiment.

FIG. 13 schematically depicts an embodiment of an electron beaminspection apparatus according to an embodiment.

FIG. 14 is a block diagram of an example computer system according to anembodiment.

FIG. 15 is a schematic diagram of another lithographic projectionapparatus according to an embodiment.

FIG. 16 is a more detailed view of the apparatus in FIG. 15 according toan embodiment.

FIG. 17 is a more detailed view of the source collector module of theapparatus of FIG. 15 and FIG. 16 according to an embodiment.

Embodiments will now be described in detail with reference to thedrawings, which are provided as illustrative examples so as to enablethose skilled in the art to practice the embodiments. Notably, thefigures and examples below are not meant to limit the scope to a singleembodiment, but other embodiments are possible by way of interchange ofsome or all of the described or illustrated elements. Whereverconvenient, the same reference numbers will be used throughout thedrawings to refer to same or like parts. Where certain elements of theseembodiments can be partially or fully implemented using knowncomponents, only those portions of such known components that arenecessary for an understanding of the embodiments will be described, anddetailed descriptions of other portions of such known components will beomitted so as not to obscure the description of the embodiments. In thepresent specification, an embodiment showing a singular component shouldnot be considered limiting; rather, the scope is intended to encompassother embodiments including a plurality of the same component, andvice-versa, unless explicitly stated otherwise herein. Moreover, thereis no intention for any term in the specification or claims to beascribed an uncommon or special meaning unless explicitly set forth assuch. Further, the scope encompasses present and future knownequivalents to the components referred to herein by way of illustration.

DETAILED DESCRIPTION

Before describing embodiments in detail, it is instructive to present anexample environment in which embodiments may be implemented.

FIG. 1 schematically depicts an embodiment of a lithographic apparatusLA. The apparatus comprises:

-   -   an illumination system (illuminator) IL configured to condition        a radiation beam B (e.g. ultraviolet (UV) radiation or deep        ultraviolet (DUV) radiation);    -   a support structure (e.g. a mask table) MT constructed to        support a patterning device (e.g. a mask) MA and connected to a        first positioner PM configured to accurately position the        patterning device in accordance with certain parameters;    -   a substrate table (e.g. a wafer table) WT (e.g., WTa, WTb or        both) constructed to hold a substrate (e.g. a resist-coated        wafer) W and connected to a second positioner PW configured to        accurately position the substrate in accordance with certain        parameters; and    -   a projection system (e.g. a refractive projection lens system)        PS configured to project a pattern imparted to the radiation        beam B by patterning device MA onto a target portion C (e.g.        comprising one or more dies and often referred to as fields) of        the substrate W, the projection system supported on a reference        frame (RF).

As here depicted, the apparatus is of a transmissive type (e.g.employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g. employing a programmable mirror array of a type asreferred to above, or employing a reflective mask).

The illuminator IL receives a beam of radiation from a radiation sourceSO. The source and the lithographic apparatus may be separate entities,for example when the source is an excimer laser. In such cases, thesource is not considered to form part of the lithographic apparatus andthe radiation beam is passed from the source SO to the illuminator ILwith the aid of a beam delivery system BD comprising for examplesuitable directing mirrors or a beam expander. In other cases the sourcemay be an integral part of the apparatus, for example when the source isa mercury lamp. The source SO and the illuminator IL, together with thebeam delivery system BD if required, may be referred to as a radiationsystem.

The illuminator IL may alter the intensity distribution of the beam. Theilluminator may be arranged to limit the radial extent of the radiationbeam such that the intensity distribution is non-zero within an annularregion in a pupil plane of the illuminator IL. Additionally oralternatively, the illuminator IL may be operable to limit thedistribution of the beam in the pupil plane such that the intensitydistribution is non-zero in a plurality of equally spaced sectors in thepupil plane. The intensity distribution of the radiation beam in a pupilplane of the illuminator IL may be referred to as an illumination mode.

So, the illuminator IL may comprise adjuster AM configured to adjust the(angular/spatial) intensity distribution of the beam. Generally, atleast the outer or inner radial extent (commonly referred to as σ-outerand σ-inner, respectively) of the intensity distribution in a pupilplane of the illuminator can be adjusted. The illuminator IL may beoperable to vary the angular distribution of the beam. For example, theilluminator may be operable to alter the number, and angular extent, ofsectors in the pupil plane wherein the intensity distribution isnon-zero. By adjusting the intensity distribution of the beam in thepupil plane of the illuminator, different illumination modes may beachieved. For example, by limiting the radial and angular extent of theintensity distribution in the pupil plane of the illuminator IL, theintensity distribution may have a multi-pole distribution such as, forexample, a dipole, quadrupole or hexapole distribution. A desiredillumination mode may be obtained, e.g., by inserting an optic whichprovides that illumination mode into the illuminator IL or using aspatial light modulator.

The illuminator IL may be operable alter the polarization of the beamand may be operable to adjust the polarization using adjuster AM. Thepolarization state of the radiation beam across a pupil plane of theilluminator IL may be referred to as a polarization mode. The use ofdifferent polarization modes may allow greater contrast to be achievedin the image formed on the substrate W. The radiation beam may beunpolarized. Alternatively, the illuminator may be arranged to linearlypolarize the radiation beam. The polarization direction of the radiationbeam may vary across a pupil plane of the illuminator IL. Thepolarization direction of radiation may be different in differentregions in the pupil plane of the illuminator IL. The polarization stateof the radiation may be chosen in dependence on the illumination mode.For multi-pole illumination modes, the polarization of each pole of theradiation beam may be generally perpendicular to the position vector ofthat pole in the pupil plane of the illuminator IL. For example, for adipole illumination mode, the radiation may be linearly polarized in adirection that is substantially perpendicular to a line that bisects thetwo opposing sectors of the dipole. The radiation beam may be polarizedin one of two different orthogonal directions, which may be referred toas X-polarized and Y-polarized states. For a quadrupole illuminationmode the radiation in the sector of each pole may be linearly polarizedin a direction that is substantially perpendicular to a line thatbisects that sector. This polarization mode may be referred to as XYpolarization. Similarly, for a hexapole illumination mode the radiationin the sector of each pole may be linearly polarized in a direction thatis substantially perpendicular to a line that bisects that sector. Thispolarization mode may be referred to as TE polarization.

In addition, the illuminator IL generally comprises various othercomponents, such as an integrator IN and a condenser CO. Theillumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic, electrostaticor other types of optical components, or any combination thereof, fordirecting, shaping, or controlling radiation.

Thus, the illuminator provides a conditioned beam of radiation B, havinga desired uniformity and intensity distribution in its cross section.

The support structure MT supports the patterning device in a manner thatdepends on the orientation of the patterning device, the design of thelithographic apparatus, and other conditions, such as for examplewhether or not the patterning device is held in a vacuum environment.The support structure can use mechanical, vacuum, electrostatic or otherclamping techniques to hold the patterning device. The support structuremay be a frame or a table, for example, which may be fixed or movable asrequired. The support structure may ensure that the patterning device isat a desired position, for example with respect to the projectionsystem. Any use of the terms “reticle” or “mask” herein may beconsidered synonymous with the more general term “patterning device.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a pattern in atarget portion of the substrate. In an embodiment, a patterning deviceis any device that can be used to impart a radiation beam with a patternin its cross-section so as to create a pattern in a target portion ofthe substrate. It should be noted that the pattern imparted to theradiation beam may not exactly correspond to the desired pattern in thetarget portion of the substrate, for example if the pattern includesphase-shifting features or so called assist features. Generally, thepattern imparted to the radiation beam will correspond to a particularfunctional layer in a device being created in the target portion, suchas an integrated circuit.

A patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable liquid-crystal display (LCD) panels. Masks are well knownin lithography, and include mask types such as binary, alternatingphase-shift, and attenuated phase-shift, as well as various hybrid masktypes. An example of a programmable mirror array employs a matrixarrangement of small mirrors, each of which can be individually tiltedso as to reflect an incoming radiation beam in different directions. Thetilted mirrors impart a pattern in a radiation beam, which is reflectedby the mirror matrix.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the moregeneral term “projection system”.

The projection system PS has an optical transfer function which may benon-uniform, which can affect the pattern imaged on the substrate W. Forunpolarized radiation such effects can be fairly well described by twoscalar maps, which describe the transmission (apodization) and relativephase (aberration) of radiation exiting the projection system PS as afunction of position in a pupil plane thereof. These scalar maps, whichmay be referred to as the transmission map and the relative phase map,may be expressed as a linear combination of a complete set of basisfunctions. A particularly convenient set is the Zernike polynomials,which form a set of orthogonal polynomials defined on a unit circle. Adetermination of each scalar map may involve determining thecoefficients in such an expansion. Since the Zernike polynomials areorthogonal on the unit circle, the Zernike coefficients may bedetermined by calculating the inner product of a measured scalar mapwith each Zernike polynomial in turn and dividing this by the square ofthe norm of that Zernike polynomial.

The transmission map and the relative phase map are field and systemdependent. That is, in general, each projection system PS will have adifferent Zernike expansion for each field point (i.e. for each spatiallocation in its image plane). The relative phase of the projectionsystem PS in its pupil plane may be determined by projecting radiation,for example from a point-like source in an object plane of theprojection system PS (i.e. the plane of the patterning device MA),through the projection system PS and using a shearing interferometer tomeasure a wavefront (i.e. a locus of points with the same phase). Ashearing interferometer is a common path interferometer and therefore,advantageously, no secondary reference beam is required to measure thewavefront. The shearing interferometer may comprise a diffractiongrating, for example a two dimensional grid, in an image plane of theprojection system (i.e. the substrate table WT) and a detector arrangedto detect an interference pattern in a plane that is conjugate to apupil plane of the projection system PS. The interference pattern isrelated to the derivative of the phase of the radiation with respect toa coordinate in the pupil plane in the shearing direction. The detectormay comprise an array of sensing elements such as, for example, chargecoupled devices (CCDs).

The projection system PS of a lithography apparatus may not producevisible fringes and therefore the accuracy of the determination of thewavefront can be enhanced using phase stepping techniques such as, forexample, moving the diffraction grating. Stepping may be performed inthe plane of the diffraction grating and in a direction perpendicular tothe scanning direction of the measurement. The stepping range may be onegrating period, and at least three (uniformly distributed) phase stepsmay be used. Thus, for example, three scanning measurements may beperformed in the y-direction, each scanning measurement being performedfor a different position in the x-direction. This stepping of thediffraction grating effectively transforms phase variations intointensity variations, allowing phase information to be determined. Thegrating may be stepped in a direction perpendicular to the diffractiongrating (z direction) to calibrate the detector.

The diffraction grating may be sequentially scanned in two perpendiculardirections, which may coincide with axes of a co-ordinate system of theprojection system PS (x and y) or may be at an angle such as 45 degreesto these axes. Scanning may be performed over an integer number ofgrating periods, for example one grating period. The scanning averagesout phase variation in one direction, allowing phase variation in theother direction to be reconstructed. This allows the wavefront to bedetermined as a function of both directions.

The transmission (apodization) of the projection system PS in its pupilplane may be determined by projecting radiation, for example from apoint-like source in an object plane of the projection system PS (i.e.the plane of the patterning device MA), through the projection system PSand measuring the intensity of radiation in a plane that is conjugate toa pupil plane of the projection system PS, using a detector. The samedetector as is used to measure the wavefront to determine aberrationsmay be used.

The projection system PS may comprise a plurality of optical (e.g.,lens) elements and may further comprise an adjustment mechanism AMconfigured to adjust one or more of the optical elements so as tocorrect for aberrations (phase variations across the pupil planethroughout the field). To achieve this, the adjustment mechanism may beoperable to manipulate one or more optical (e.g., lens) elements withinthe projection system PS in one or more different ways. The projectionsystem may have a co-ordinate system wherein its optical axis extends inthe z direction. The adjustment mechanism may be operable to do anycombination of the following: displace one or more optical elements;tilt one or more optical elements; or deform one or more opticalelements. Displacement of an optical element may be in any direction (x,y, z or a combination thereof). Tilting of an optical element istypically out of a plane perpendicular to the optical axis, by rotatingabout an axis in the x or y directions although a rotation about the zaxis may be used for a non-rotationally symmetric aspherical opticalelement. Deformation of an optical element may include a low frequencyshape (e.g. astigmatic) or a high frequency shape (e.g. free formaspheres). Deformation of an optical element may be performed forexample by using one or more actuators to exert force on one or moresides of the optical element or by using one or more heating elements toheat one or more selected regions of the optical element. In general, itmay not be possible to adjust the projection system PS to correct forapodization (transmission variation across the pupil plane). Thetransmission map of a projection system PS may be used when designing apatterning device (e.g., mask) MA for the lithography apparatus LA.Using a computational lithography technique, the patterning device MAmay be designed to at least partially correct for apodization.

The lithographic apparatus may be of a type having two (dual stage) ormore tables (e.g., two or more substrate tables WTa, WTb, two or morepatterning device tables, a substrate table WTa and a table WTb belowthe projection system without a substrate that is dedicated to, forexample, facilitating measurement, or cleaning, etc.). In such “multiplestage” machines the additional tables may be used in parallel, orpreparatory steps may be carried out on one or more tables while one ormore other tables are being used for exposure. For example, alignmentmeasurements using an alignment sensor AS or level (height, tilt, etc.)measurements using a level sensor LS may be made.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g. water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the patterning device and the projection system. Immersiontechniques are well known in the art for increasing the numericalaperture of projection systems. The term “immersion” as used herein doesnot mean that a structure, such as a substrate, must be submerged inliquid, but rather only means that liquid is located between theprojection system and the substrate during exposure.

So, in operation of the lithographic apparatus, a radiation beam isconditioned and provided by the illumination system IL. The radiationbeam B is incident on the patterning device (e.g., mask) MA, which isheld on the support structure (e.g., mask table) MT, and is patterned bythe patterning device. Having traversed the patterning device MA, theradiation beam B passes through the projection system PS, which focusesthe beam onto a target portion C of the substrate W. With the aid of thesecond positioner PW and position sensor IF (e.g. an interferometricdevice, linear encoder, 2-D encoder or capacitive sensor), the substratetable WT can be moved accurately, e.g. so as to position differenttarget portions C in the path of the radiation beam B. Similarly, thefirst positioner PM and another position sensor (which is not explicitlydepicted in FIG. 1 ) can be used to accurately position the patterningdevice MA with respect to the path of the radiation beam B, e.g. aftermechanical retrieval from a mask library, or during a scan. In general,movement of the support structure MT may be realized with the aid of along-stroke module (coarse positioning) and a short-stroke module (finepositioning), which form part of the first positioner PM. Similarly,movement of the substrate table WT may be realized using a long-strokemodule and a short-stroke module, which form part of the secondpositioner PW. In the case of a stepper (as opposed to a scanner) thesupport structure MT may be connected to a short-stroke actuator only,or may be fixed. Patterning device MA and substrate W may be alignedusing patterning device alignment marks M1, M2 and substrate alignmentmarks P1, P2. Although the substrate alignment marks as illustratedoccupy dedicated target portions, they may be located in spaces betweentarget portions (these are known as scribe-lane alignment marks).Similarly, in situations in which more than one die is provided on thepatterning device MA, the patterning device alignment marks may belocated between the dies.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the support structure MT and the substrate table WT arekept essentially stationary, while an entire pattern imparted to theradiation beam is projected onto a target portion C at one time (i.e. asingle static exposure). The substrate table WT is then shifted in the Xor Y direction so that a different target portion C can be exposed. Instep mode, the maximum size of the exposure field limits the size of thetarget portion C imaged in a single static exposure.

2. In scan mode, the support structure MT and the substrate table WT arescanned synchronously while a pattern imparted to the radiation beam isprojected onto a target portion C (i.e. a single dynamic exposure). Thevelocity and direction of the substrate table WT relative to the supportstructure MT may be determined by the (de-)magnification and imagereversal characteristics of the projection system PS. In scan mode, themaximum size of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.

3. In another mode, the support structure MT is kept essentiallystationary holding a programmable patterning device, and the substratetable WT is moved or scanned while a pattern imparted to the radiationbeam is projected onto a target portion C. In this mode, generally apulsed radiation source is employed and the programmable patterningdevice is updated as required after each movement of the substrate tableWT or in between successive radiation pulses during a scan. This mode ofoperation can be readily applied to maskless lithography that utilizesprogrammable patterning device, such as a programmable mirror array of atype as referred to above.

Combinations or variations on the above described modes of use orentirely different modes of use may also be employed.

Although specific reference may be made in this text to the use oflithography apparatus in the manufacture of ICs, it should be understoodthat the lithography apparatus described herein may have otherapplications, such as the manufacture of integrated optical systems,guidance and detection patterns for magnetic domain memories,liquid-crystal displays (LCDs), thin film magnetic heads, etc. Theskilled artisan will appreciate that, in the context of such alternativeapplications, any use of the terms “wafer” or “die” herein may beconsidered as synonymous with the more general terms “substrate” or“target portion”, respectively. The substrate referred to herein may beprocessed, before or after exposure, in for example a track (a tool thattypically applies a layer of resist to a substrate and develops theexposed resist) or a metrology or inspection tool. Where applicable, thedisclosure herein may be applied to such and other substrate processingtools. Further, the substrate may be processed more than once, forexample in order to create a multi-layer IC, so that the term substrateused herein may also refer to a substrate that already contains multipleprocessed layers.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.having a wavelength of 365, 248, 193, 157 or 126 nm) and extremeultra-violet (EUV) radiation (e.g. having a wavelength in the range of5-20 nm), as well as particle beams, such as ion beams or electronbeams.

Various patterns on or provided by a patterning device may havedifferent process windows. i.e., a space of processing variables underwhich a pattern will be produced within specification. Examples ofpattern specifications that relate to potential systematic defectsinclude checks for necking, line pull back, line thinning, criticaldimension (CD), edge placement, overlapping, resist top loss, resistundercut or bridging. The process window of all the patterns on apatterning device or an area thereof may be obtained by merging (e.g.,overlapping) process windows of each individual pattern. The boundary ofthe process window of all the patterns contains boundaries of processwindows of some of the individual patterns. In other words, theseindividual patterns limit the process window of all the patterns. Thesepatterns can be referred to as “hot spots” or “process window limitingpatterns (PWLPs),” which are used interchangeably herein. Whencontrolling a part of a patterning process, it is possible andeconomical to focus on the hot spots. When the hot spots are notdefective, it is most likely that all the patterns are not defective.

As shown in FIG. 2 , the lithographic apparatus LA may form part of alithographic cell LC, also sometimes referred to a lithocell or cluster,which also includes apparatuses to perform pre- and post-exposureprocesses on a substrate. Conventionally these include one or more spincoaters SC to deposit one or more resist layers, one or more developersDE to develop exposed resist, one or more chill plates CH or one or morebake plates BK. A substrate handler, or robot, RO picks up one or moresubstrates from input/output port I/O1, I/O2, moves them between thedifferent process apparatuses and delivers them to the loading bay LB ofthe lithographic apparatus. These apparatuses, which are oftencollectively referred to as the track, are under the control of a trackcontrol unit TCU which is itself controlled by the supervisory controlsystem SCS, which also controls the lithographic apparatus vialithography control unit LACU. Thus, the different apparatuses can beoperated to maximize throughput and processing efficiency.

In order that a substrate that is exposed by the lithographic apparatusis exposed correctly and consistently or in order to monitor a part ofthe patterning process (e.g., a device manufacturing process) thatincludes at least one pattern transfer step (e.g., an opticallithography step), it is desirable to inspect a substrate or otherobject to measure or determine one or more properties such as alignment,overlay (which can be, for example, between structures in overlyinglayers or between structures in a same layer that have been providedseparately to the layer by, for example, a double patterning process),line thickness, critical dimension (CD), focus offset, a materialproperty, etc. Accordingly a manufacturing facility in which lithocellLC is located also typically includes a metrology system MET whichmeasures some or all of the substrates W that have been processed in thelithocell or other objects in the lithocell. The metrology system METmay be part of the lithocell LC, for example it may be part of thelithographic apparatus LA (such as alignment sensor AS).

The one or more measured parameters may include, for example, overlaybetween successive layers formed in or on the patterned substrate,critical dimension (CD) (e.g., critical linewidth) of, for example,features formed in or on the patterned substrate, focus or focus errorof an optical lithography step, dose or dose error of an opticallithography step, optical aberrations of an optical lithography step,etc. This measurement may be performed on a target of the productsubstrate itself or on a dedicated metrology target provided on thesubstrate. The measurement can be performed after-development of aresist but before etching or can be performed after-etch.

There are various techniques for making measurements of the structuresformed in the patterning process, including the use of a scanningelectron microscope, an image-based measurement tool or variousspecialized tools. As discussed above, a fast and non-invasive form ofspecialized metrology tool is one in which a beam of radiation isdirected onto a target on the surface of the substrate and properties ofthe scattered (diffracted/reflected) beam are measured. By evaluatingone or more properties of the radiation scattered by the substrate, oneor more properties of the substrate can be determined. This may betermed diffraction-based metrology. One such application of thisdiffraction-based metrology is in the measurement of feature asymmetrywithin a target. This can be used as a measure of overlay, for example,but other applications are also known. For example, asymmetry can bemeasured by comparing opposite parts of the diffraction spectrum (forexample, comparing the −1st and +1st orders in the diffraction spectrumof a periodic grating). This can be done as described above and asdescribed, for example, in U.S. patent application publication US2006-066855, which is incorporated herein in its entirety by reference.Another application of diffraction-based metrology is in the measurementof feature width (CD) within a target. Such techniques can use theapparatus and methods described hereafter.

Thus, in a device fabrication process (e.g., a patterning process or alithography process), a substrate or other objects may be subjected tovarious types of measurement during or after the process. Themeasurement may determine whether a particular substrate is defective,may establish adjustments to the process and apparatuses used in theprocess (e.g., aligning two layers on the substrate or aligning thepatterning device to the substrate), may measure the performance of theprocess and the apparatuses, or may be for other purposes. Examples ofmeasurement include optical imaging (e.g., optical microscope),non-imaging optical measurement (e.g., measurement based on diffractionsuch as ASML YieldStar metrology tool, ASML SMASH metrology system),mechanical measurement (e.g., profiling using a stylus, atomic forcemicroscopy (AFM)), or non-optical imaging (e.g., scanning electronmicroscopy (SEM)). The SMASH (SMart Alignment Sensor Hybrid) system, asdescribed in U.S. Pat. No. 6,961,116, which is incorporated by referenceherein in its entirety, employs a self-referencing interferometer thatproduces two overlapping and relatively rotated images of an alignmentmarker, detects intensities in a pupil plane where Fourier transforms ofthe images are caused to interfere, and extracts the positionalinformation from the phase difference between diffraction orders of thetwo images which manifests as intensity variations in the interferedorders.

Metrology results may be provided directly or indirectly to thesupervisory control system SCS. If an error is detected, an adjustmentmay be made to exposure of a subsequent substrate (especially if theinspection can be done soon and fast enough that one or more othersubstrates of the batch are still to be exposed) or to subsequentexposure of the exposed substrate. Also, an already exposed substratemay be stripped and reworked to improve yield, or discarded, therebyavoiding performing further processing on a substrate known to befaulty. In a case where only some target portions of a substrate arefaulty, further exposures may be performed only on those target portionswhich are good.

Within a metrology system MET, a metrology apparatus is used todetermine one or more properties of the substrate, and in particular,how one or more properties of different substrates vary or differentlayers of the same substrate vary from layer to layer. As noted above,the metrology apparatus may be integrated into the lithographicapparatus LA or the lithocell LC or may be a stand-alone device.

To enable the metrology, one or more targets can be provided on thesubstrate. In an embodiment, the target is specially designed and maycomprise a periodic structure. In an embodiment, the target is a part ofa device pattern, e.g., a periodic structure of the device pattern. Inan embodiment, the device pattern is a periodic structure of a memorydevice (e.g., a Bipolar Transistor (BPT), a Bit Line Contact (BLC), etc.structure).

In an embodiment, the target on a substrate may comprise one or more 1-Dperiodic structures (e.g., gratings), which are printed such that afterdevelopment, the periodic structural features are formed of solid resistlines. In an embodiment, the target may comprise one or more 2-Dperiodic structures (e.g., gratings), which are printed such that afterdevelopment, the one or more periodic structures are formed of solidresist pillars or vias in the resist. The bars, pillars or vias mayalternatively be etched into the substrate (e.g., into one or morelayers on the substrate).

In an embodiment, one of the parameters of interest of a patterningprocess is overlay. Overlay can be measured using dark fieldscatterometry in which the zeroth order of diffraction (corresponding toa specular reflection) is blocked, and only higher orders processed.Examples of dark field metrology can be found in PCT patent applicationpublication nos. WO 2009/078708 and WO 2009/106279, which are herebyincorporated in their entirety by reference. Further developments of thetechnique have been described in U.S. patent application publicationsUS2011-0027704, US2011-0043791 and US2012-0242970, which are herebyincorporated in their entirety by reference. Diffraction-based overlayusing dark-field detection of the diffraction orders enables overlaymeasurements on smaller targets. These targets can be smaller than theillumination spot and may be surrounded by device product structures ona substrate. In an embodiment, multiple targets can be measured in oneradiation capture.

FIG. 3 schematically depicts a method of predicting defects in a devicemanufacturing process. Examples of a defect can include necking,line-end pull back, line thinning, incorrect CD, overlapping, bridgingand/or others. A defect can be in a resist image, an optical image or anetch image (i.e., a pattern transferred to a layer of the substrate byetching using the resist thereon as a mask). At 313, a model is used tocompute a characteristic 314 (e.g., the existence, location, type,shape, etc.) of a pattern, based on one or more process parameters 311of the device manufacturing process and/or one or more layout parameters312. The process parameters 311 are parameters associated with thedevice manufacturing process but not with the layout. For example, theprocess parameters 311 may include a characteristic of the illumination(e.g., intensity, pupil profile, etc.), a characteristic of theprojection optics, dose, focus, a characteristic of the resist, acharacteristic of development of the resist, a characteristic ofpost-exposure baking of the resist, and/or a characteristic of etching.The layout parameters 312 may include a shape, size, relative location,and/or absolute location of various features on a layout, and/oroverlapping of features on different layouts. In an example, the modelis an empirical model, where the pattern, which can be in a resistimage, aerial image, or etch image, is not simulated; instead, theempirical model determines the characteristic 314 (e.g., the existence,location, type, shape, etc.) of the pattern based on a correlationbetween the input (e.g., the one or more process parameters 311 and/orlayout parameters 312) of the empirical model and the characteristic. Inan example, the model is a computational model, where at least a portionof the pattern is simulated and the characteristic 314 is determinedfrom the portion, or the characteristic 314 is simulated withoutsimulating the pattern itself. At 315, whether the pattern is a defector whether there is a probability that the pattern is a defect isdetermined based on the characteristic 314. For example, a line-end pullback defect may be identified by finding a line end too far away fromits desired location; a bridging defect may be identified by finding alocation where two lines undesirably join.

Examples of applicable computational methods are described in U.S.patent application publication no. US 2015-0227654, PCT patentapplication publication no. WO 2016-128189, PCT patent applicationpublication no. WO 2016-202546, PCT patent application publication no.WO 2017-114662 and PCT patent application publ. no. WO 2018-015181, eachof which is incorporated herein in its entirety by reference.

In an embodiment, the model can be in the form of a polynomialcomprising, as variables, one or more process parameters of the devicemanufacturing process. For example, the polynomial can be characterizedin terms of one or more selected from: focus, dose, a moving average(MA) of lithographic apparatus table servo error, moving standarddeviation (MSD) of a lithographic apparatus table servo error, apatterning device pattern error, and/or an etch parameter. In anembodiment, one or more variables can be characterized spatially (e.g.,with X and Y coordinates, with radial coordinates, etc.) across thesubstrate. As an example, the polynomial can be specified in terms of atleast focus and dose, wherein the focus and dose is spatiallycharacterized across the substrate.

An exemplary flow chart of a method of modelling and/or simulating partsof a patterning process is illustrated in FIG. 4 , for example,modelling and/or simulating at least a portion of a pattern or acharacteristic of a pattern in an image (e.g., resist image, aerialimage, etch image). As will be appreciated, the models may represent adifferent patterning process and need not comprise all the modelsdescribed below.

As described above, in a lithographic projection apparatus, anillumination system provides illumination (i.e. radiation) to patterningdevice and projection optics directs the illumination from thepatterning device onto a substrate. So, in an embodiment, the projectionoptics enables the formation of an aerial image (AI), which is theradiation intensity distribution at the substrate. A resist layer on thesubstrate is exposed and the aerial image is transferred to the resistlayer as a latent “resist image” (RI) therein. The resist image (RI) canbe defined as a spatial distribution of solubility of the resist in theresist layer. In an embodiment, simulation of a lithography process cansimulate the production of the aerial image and/or resist image.

An illumination model 31 represents optical characteristics (includingradiation intensity distribution and/or phase distribution) of anillumination mode used to generate a patterned radiation beam. Theillumination model 31 can represent the optical characteristics of theillumination that include, but not limited to, numerical aperturesettings, illumination sigma (a) settings as well as any particularillumination mode shape (e.g. off-axis radiation shape such as annular,quadrupole, dipole, etc.), where a (or sigma) is outer radial extent ofthe illuminator.

A projection optics model 32 represents optical characteristics(including changes to the radiation intensity distribution and/or thephase distribution caused by the projection optics) of the projectionoptics. The projection optics model 32 may include optical aberrationscaused by various factors, for example, heating of the components of theprojection optics, stress caused by mechanical connections of thecomponents of the projection optics, etc. The projection optics model 32can represent the optical characteristics of the projection optics,including one or more selected from: an aberration, a distortion, arefractive index, a physical size, a physical dimension, an absorption,etc. Optical properties of the lithographic projection apparatus (e.g.,properties of the illumination, the patterning device pattern and theprojection optics) dictate the aerial image. Since the patterning devicepattern used in the lithographic projection apparatus can be changed, itis desirable to separate the optical properties of the patterning devicepattern from the optical properties of the rest of the lithographicprojection apparatus including at least the illumination and theprojection optics. The illumination model 31 and the projection opticsmodel 32 can be combined into a transmission cross coefficient (TCC)model.

A patterning device pattern model 33 represents optical characteristics(including changes to the radiation intensity distribution and/or thephase distribution caused by a given patterning device pattern) of apatterning device pattern (e.g., a device design layout corresponding toa feature of an integrated circuit, a memory, an electronic device,etc.), which is the representation of an arrangement of features on orformed by a patterning device. The patterning device model 33 captureshow the design features are laid out in the pattern of the patterningdevice and may include a representation of detailed physical propertiesof the patterning device and a patterning device pattern, as described,for example, in U.S. Pat. No. 7,587,704, which is incorporated herein inits entirety by reference.

A resist model 37 can be used to calculate the resist image from theaerial image. An example of such a resist model can be found in U.S.Pat. No. 8,200,468, which is hereby incorporated by reference in itsentirety. The resist model typically describes the effects of chemicalprocesses which occur during resist exposure, post exposure bake (PEB)and development, in order to predict, for example, contours of resistfeatures formed on the substrate and so it typically is related only tosuch properties of the resist layer (e.g., effects of chemical processeswhich occur during exposure, post-exposure bake and development). In anembodiment, the optical properties of the resist layer, e.g., refractiveindex, film thickness, propagation and polarization effects—may becaptured as part of the projection optics model 32.

Having these models, an aerial image 36 can be simulated from theillumination model 31, the projection optics model 32 and the patterningdevice pattern model 33. An aerial image (AI) is the radiation intensitydistribution at substrate level. Optical properties of the lithographicprojection apparatus (e.g., properties of the illumination, thepatterning device and the projection optics) dictate the aerial image.

As noted above, a resist layer on a substrate is exposed by the aerialimage and the aerial image is transferred to the resist layer as alatent “resist image” (RI) therein. A resist image 38 can be simulatedfrom the aerial image 36 using a resist model 37. So, in general, theconnection between the optical and the resist model is a simulatedaerial image intensity within the resist layer, which arises from theprojection of radiation onto the substrate, refraction at the resistinterface and multiple reflections in the resist film stack. Theradiation intensity distribution (aerial image intensity) is turned intoa latent “resist image” by absorption of incident energy, which isfurther modified by diffusion processes and various loading effects.Efficient simulation methods that are fast enough for full-chipapplications approximate the realistic 3-dimensional intensitydistribution in the resist stack by a 2-dimensional aerial (and resist)image.

In an embodiment, the resist image can be used as an input to apost-pattern transfer process model 39. The post-pattern transferprocess model 39 defines performance of one or more post-resistdevelopment processes (e.g., etch, CMP, etc.) and can produce apost-etch image 40. That is, an etch image 40 can be simulated from theresist image 38 using a post-pattern transfer process model 39.

Thus, this model formulation describes most, if not all, of the knownphysics and chemistry of the overall process, and each of the modelparameters desirably corresponds to a distinct physical or chemicaleffect. The model formulation thus sets an upper bound on how well themodel can be used to simulate the overall manufacturing process.

Simulation of the patterning process can, for example, predict contours,CDs, edge placement (e.g., edge placement error), pattern shift, etc. inthe aerial, resist and/or etch image. That is, the aerial image 36, theresist image 38 or the etch image 40 may be used to determine acharacteristic (e.g., the existence, location, type, shape, etc. of) ofa pattern. Thus, the objective of the simulation is to accuratelypredict, for example, edge placement, and/or contours, and/or patternshift, and/or aerial image intensity slope, and/or CD, etc. of theprinted pattern. These values can be compared against an intended designto, e.g., correct the patterning process, identify where a defect ispredicted to occur, etc. The intended design is generally defined as apre-OPC design layout which can be provided in a standardized digitalfile format such as GDSII or OASIS or other file format.

Details of techniques and models used to transform a patterning devicepattern into various lithographic images (e.g., an aerial image, aresist image, etc.), apply OPC using those techniques and models andevaluate performance (e.g., in terms of process window) are described inU.S. Patent Application Publication Nos. US 2008-0301620, 2007-0050749,2007-0031745, 2008-0309897, 2010-0162197, 2010-0180251 and 2011-0099526,the disclosure of each which is hereby incorporated by reference in itsentirety.

To facilitate the speed of evaluating the models, from the patterningdevice pattern, one or more portions may be identified, which arereferred to as “clips.” In a specific embodiment, a set of clips isextracted, which represents the complicated patterns in the patterningdevice pattern (typically about 50 to 1000 clips, although any number ofclips may be used). As will be appreciated by those skilled in the art,these patterns or clips represent small portions (i.e. circuits, cellsor patterns) of the design and especially the clips represent smallportions for which particular attention and/or verification is needed.In other words, clips may be the portions of the patterning devicepattern or may be similar or have a similar behavior of portions of thepatterning device pattern where critical features are identified eitherby experience (including clips provided by a customer), by trial anderror, or by running a full-chip simulation. Clips usually contain oneor more test patterns or gauge patterns. An initial larger set of clipsmay be provided a priori by a customer based on known critical featureareas in a patterning device pattern which require particularconsideration. In an embodiment, the initial larger set of clips may beextracted from the entire patterning device pattern by using some kindof automated (such as, machine vision) or manual algorithm thatidentifies the critical feature areas.

Furthermore, various patterns on or provided by a patterning device mayhave different process windows. i.e., a space of processing variablesunder which a pattern will be produced within specification. Examples ofpattern specifications that relate to potential systematic defectsinclude checks for necking, line-end pull back, line thinning, CD, edgeplacement, overlapping, resist top loss, resist undercut and/orbridging. The process window of all the patterns on a patterning deviceor an area thereof may be obtained by merging (e.g., overlapping)process windows of each individual pattern. The boundary of the processwindow of all the patterns contains boundaries of process windows ofsome of the individual patterns. In other words, these individualpatterns limit the process window of all the patterns. These patternscan be referred to as “hot spots” or “process window limiting patterns(PWLPs),” which are used interchangeably herein. When designing,modifying, etc. a part of a patterning process using, for example, themodeling described herein, it is possible and economical to focus on thehot spots. When the hot spots are not defective, it is most likely thatall the patterns are not defective.

So, a current approach to identifying actual defects on substrates basedon relatively fast optical inspection can run into resolution problemsin trying to detect small defects (e.g., sub-10 nm defects). On theother hand, e-beam systems are typically too slow to be used inhigh-volume manufacturing (HVM) to inspect a high number of locationsfor defects. So, as described above, computational methods can be usedto help identify locations where defects should be located on substratesand then guiding an e-beam inspection (EBI) tool to those locations.This can increase the effective inspection speed of EBI and making ituseful for finding small defects (e.g., sub-10 nm defects) in HVM.

Of course, the effectiveness of using a computational method to identifypotential defects to improve the inspection speed depends on the modelused to guide the EBI tool to relevant defect locations with highaccuracy. But a problem faced by such computational methods in findingsmall defects (e.g., sub-10 nm defects) is that the modelling used toidentify defect locations cannot predict perfectly how patterns will beproduced on product substrates. As a result, there is a model residual,namely a difference between the predicted size of a pattern and that asmeasured.

These model residuals (e.g., noise) can be commensurate in size with thesmall defects that the computational methods attempt to predict. Thisresults in significant uncertainty about whether a defect will or willnot manifest itself at the predicted locations. So, to reach anacceptable level of certainty of finding all defects on a substrateduring inspection, the EBI tool should visit all the locations that thecomputational method indicates that there is a fair chance that a defectis present; that is the thresholding used to identify defects may needto be wider than optimal in order to be sure to capture all, or most,defects. This means that the EBI tool will have to inspect a sizeablenumber of unnecessary locations (nuisance) in order to capture the realdefects. This is likely to result in unnecessary inspection time andpoor correlation between the number of points measured and the actualnumber of defects. That is, for example, the number of points that wouldneed to be sampled on any given substrate to ascertain the actual numberof defects is significantly larger than the actual number of defects andits ratio to the actual number of defects on any given substrate is notnecessarily a constant. So, the inspection time can be significantlylonger than needed.

Now, although random variations are random, their statistics may not be.Therefore, predicting defects statistically, in other words, predictingthe probabilities of defects, may be possible. Accordingly, in anembodiment, a probabilistic model or method, i.e., a model or methodthat computes a probability of the characteristic of defects having acertain value, is used at 313 of FIG. 3 . For example, the probabilisticmodel or method can predict the probability that a pattern in an imagehas a certain shape or a certain CD. A probabilistic model or method maybetter capture random variations in the device manufacturing processthan only use of a non-probabilistic model.

Examples of probabilistic model are discussed in PCT patent applicationpublication numbers WO 2019-011604 and WO 2019-115426, each of which isincorporated herein in its entirety by reference. Specifically, themethods in the aforementioned US applications involve adding aprobabilistic model based on the statistics of a characteristic (e.g.,CD, hotspots) measured on a substrate (interchangeably referred to aswafer) and allowing for two different concentric zones on which thesestatistics are collected on the substrate. However, this limits theusefulness of the probabilistic model to a predefined (i.e. notadaptable) substrate distribution of the characteristic (e.g.,hotspots). Such probabilistic model may result in a higher samplingcount (and thus longer inspection time) for finding more than 90% of thedefects on a substrate.

The present disclosure provides methods and probabilistic model thatallows the probabilistic model to be based on statistics that areadapted to the substrate spatial-characteristics of the characteristic(e.g., hotspots) response to the patterning process.

FIG. 5 is a flow chart of a method 500 for determining a probabilisticmodel configured to predict a characteristic of a pattern on a substratesubjected to a patterning process. According to the method 500, aprobabilistic model is configured to predict a characteristic of asubstrate such as a probability of a defect at a particular location onthe substrate, hotspots, CD, etc. In an embodiment, the probabilisticmodel is developed based on spatial-characteristics of the substratesuch as spatial characteristics of hotspots. Such characteristicsrelates to a distribution of a residue (e.g., a difference betweenpredicted and measured characteristics of a substrate) across thesubstrate. There may be a significant variation in the distribution ofthe residue across the substrate, as such the probabilistic model isdefined per zone of the substrate. A zone is a region of on a substratehaving a particular variation in residue. Thus, according to anembodiment, a substrate may be divided into a plurality of zones, eachzone associated with a probabilistic model. Furthermore, theprobabilistic model may be adapted or modified based on additional datarelated to a desired characteristic of a substrate or patterns thereonobtained from subsequently processed substrates. For example, based onthe additional data the zones of the substrate may be redefined andthereby the corresponding probabilistic model per zone maycorrespondingly be redefined.

Thus, based on the location being measured, appropriate probabilisticmodel may be selected resulting in more accurate predictions of defects,which in turn can be used to guide the metrology tool for makingmeasurements. The method 500 is discussed in more detail hereinafter.

The method 500, in process P52, involves obtaining a spatial map 501 ofa distribution of a residue corresponding to the characteristic of thesubstrate. In an embodiment, there is a difference between a computedvalue of a characteristic of the pattern (e.g., obtained by simulationof a process model which may be a non-probabilistic model, aphysics-based model, empirical model, etc.) and an actual value of thecharacteristic of the pattern as produced by the patterning process.This difference is called a residue. The residue may be attributed to,for example, random variations, imperfection of the non-probabilisticmodel, an input of the non-probabilistic model, or a combinationthereof.

In practice, the residue may have a distribution (e.g., distribution 611in FIG. 6 , and distributions 852 and 862 in FIGS. 8A and 8C)characterized, for example, in term of the number of instances of theoccurrence of residue values, in terms of probabilities of theoccurrence of the residue values, etc. For example, a particular patternmay in practice be produced at different sizes across a substrate, butthe predicted size of those pattern instances across the substrate couldbe the same or be predicted with a different variation than the actualproduced sizes. Accordingly, there would be a distribution of theresidue values.

In an embodiment, an attribute of the distribution of the residue may beobtained. In an embodiment, an attribute is one that represents thespread of the distribution (e.g., variance and/or standard deviation).In an embodiment, the attribute is for a particular pattern type orcollection of pattern types. In an embodiment, the attribute is for aparticular hotspot or a collection of hotspots. As will be appreciated,a plurality of different attributes can be obtained, each correspondingto a different pattern type or collection of pattern types.

One example of the attribute is a probability density function (PDF) ofthe residue. In an embodiment, the PDF can be normalized so that the sumof the probabilities under the distribution is a particular value,e.g., 1. A further example of the attribute is a cumulative distributionfunction (CDF) of the residue or an empirical cumulative distributionfunction (eCDF) (also called an empirical distribution function (EDF)).The eCDF may be determined from the values of the residue. An eCDF isthe distribution function associated with the empirical measure of asample (e.g., the values of the residue obtained from a plurality ofpattern instances as discussed below). The eCDF is a step function. TheeCDF may be defined using the following formula:

${{\hat{F}(t)} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}I_{x_{i} \leq t}}}},$where (x1, . . . , xn) are the values in the sample, and I_(A) is anindicator function of event A. The value of the eCDF {circumflex over(F)}(t) at any specified value t is the fraction of the sample that isless than or equal to t. It converges with probability 1 to thatunderlying distribution with increasing n, according to theGlivenko-Cantelli theorem. The CDF may be estimated based on an eCDF.For example, the CDF F(t) may be estimated based on the eCDF {circumflexover (F)}(t) using, for example, the Dvorestzky-Kiefer-Wolfowitz (DKW)inequality. The estimation error E of the CDF based on the eCDF isbounded by the DKW inequality:

${{\mathbb{p}}\{ {{\sup\limits_{t}{{{F(t)} - {\hat{F}(t)}}}} > \epsilon} \}} \leq {2\;{e^{{- 2}\; n\;\epsilon^{2}}.}}$The DKW inequality shows that the estimation error ∈ may be determinedby the number of the values of the residue n used to construct the eCDF{circumflex over (F)}(t).

A spatial map refers to a distribution of the residue across thesubstrate. In an embodiment, each location on the spatial map may have aparticular distribution of the residue. For example, a center of thesubstrate may have a residue with a relatively low variation (e.g.,lowest variation) and another portion such as a part of an edge ofsubstrate may have residue with relatively high variation (e.g., highestvariation). FIG. 7 illustrate an example spatial map 730, where aspatial map 730 of the distribution 733 of the residue includeslocations such as 733 a, 733 b, 733 c having a first variation (e.g.,highest variation relative to other locations), and locations 733 dhaving a second variation (e.g., less than the first variation) ofresidue. In an embodiment, the first set of locations having a first(larger) variation may be grouped into one statistical sample describinga first particular area or plurality of areas on the wafer, whereas asecond set of locations having a second (smaller) variation may begrouped into one statistical sample describing a second particular areaor plurality of areas on the wafer. In an embodiment, the spatial map501 of the residue may be obtained, for example, as discussed in FIG. 5. In FIG. 6 , a spatial map 630 includes the distribution of the residuecorresponding to a characteristic (e.g., CD) of a pattern on thesubstrate.

A characteristic of a substrate refers to a value of a characteristic ofa pattern on the substrate. The characteristic of the substrate may bedetermined based on simulation of the patterning process or based onmeasurement obtained from a metrology tool. In an embodiment, anon-probabilistic model may be defined to predict the characteristic ofthe substrate. A non-exhaustive list of examples of the characteristicmay include one or more selected from: position relative to thesubstrate, position relative to one or more other pattern instances onthe substrate, a geometric size (e.g., a CD), a geometric shape, and/ora measure of a stochastic effect (e.g., CD uniformity (CDU), line widthroughness (LWR), etc.). In an embodiment, the value is calculated for atype of pattern for which there is an attribute (e.g., it matches thepattern type for the attribute or matches to a collection of patterntypes for the attribute).

The method 500, in process P54, involves determining, via a computingsystem (e.g., system 100 of FIG. 14 ), a zone 542 of the spatial map 501based on an attribute of the distribution of the residue within thespatial map 501. In an embodiment, a zone 542 refers to a region of thespatial map 501 having a particular variation in the distribution of theresidue. In an embodiment, the spatial map 501 of the residue may bedivided into a plurality of zones, each zone have a variation of theresidue different from the other. In an embodiment, the zone 542 may bea single region or the zone 542 may be a set of discrete regions spreadat different locations on the substrate. An example of zones isillustrated in FIG. 9 , where a first zone Z1 includes two regions alongan edge of the substrate, as shown, and a second zone Z2 is a singleregion adjacent to the first zone.

In an embodiment, determining the zone 542 involves determining whetherthe variation of the distribution of the residue exceeds a predefinedthreshold. For example, the variation in the distribution of the residuemay change in a radial direction as one moves from a center to the edgeof the substrate. For example, the different zones can be defined bycomparing the 1σ variation values for the different areas on the wafers.If the 1σ variation values differ significantly from one area of thewafer to the other, then two zones can be defined. In another example, adifferent statistical descriptor than variation may be used. Forexample, a statistical descriptor may be related to a range of thepopulation in certain areas of the wafer: if the values for the rangeare significantly different, e.g., between the center and the edge ofthe wafer, then two discrete zones can be defined. In an embodiment, apredefined threshold may be in terms of CD values. Furthermore, theprocess P54 involves, responsive to the variation the exceeding of thepredefined threshold, defining a different zone. For example, a regionaround the center portion having 1σ variation may be considered a firstzone and another region around the edge portion having 3σ variation maybe defined as a second zone.

In an embodiment, the determining the zone 542 is an iterative process.In the iterative process a plurality of zones are obtained based on thevariation of the distribution of the residue, such that a first zone ofthe plurality of zones has a first variation of the distribution of theresidue, and a second zone of the plurality of zones has a secondvariation in the distribution of the residue. In an embodiment aniteration of determining the zone involves identifying boundaries ofeach of a plurality of zones based on a clustering algorithm or aclassification algorithm.

For example, in an embodiment, the determining of the zone 542 involvesexecuting a classification algorithm with the spatial map 501 of thedistribution of the residue as input. The classification algorithmoutputs one or more groups of the residue based on the variation in theresidue. Further, a boundary around each group of the one or more groupsof residue is identified, where a zone 542 is a region within theboundary. In an embodiment, the classification algorithm is a machinelearning model trained to identify zones based on the variation in thedistribution of the residue or the variation of the characteristic ofthe printed substrate. In an embodiment, the classification algorithminvolves a clustering analysis based on at least one of: k-nearest mean,mean-shifting, naive-Bayes and back propagation neural network,Density-Based Spatial Clustering of Applications with Noise, Gaussianmixture model, or hierarchical clustering.

In an embodiment, the iteration of determining the zone further involvesmodifying the zones or a boundary of the zone(s) based on metrology datacorresponding to a characteristic of a pattern on a substrate. Forexample, the iteration involves obtaining metrology data 548 across thesubstrate. In an embodiment, the metrology data 548 may be limited to afew selected zones (e.g., zones with relatively higher variation in thedistribution of the residue). For example, the metrology datacorresponding to the characteristic of a printed substrate may beobtained within the first zone (e.g., the zone Z1 of FIG. 9 ) and thesecond zone (e.g., the zone Z2 of FIG. 9 ). In an embodiment, the firstzone and the second zone is separated by a first boundary (e.g., B1 aand B1 b in FIG. 9 ) between the first zone (e.g., Z1 in FIG. 9 ) andthe second zone, and the second zone (e.g., Z2 in FIG. 9 ) is identifiedby a second boundary (e.g., B2 in FIG. 9 ). Once the metrology data isobtained, residues may be determined, which can be further used formodifying the first boundary around the first zone of the residue.

In an embodiment, for determining of the zone (e.g., usingclassification algorithm), the process may be configured to determinethe zone in terms of radial distance from a center of the substrate. Forexample, by defining radius and theta (an angle about a center of thesubstrate) as a parameter of the classification algorithm. In anembodiment, the zone is defined as an enclosed region within anirregular boundary in a radial direction and spanning a certain angularregion of the substrate. For example, zones Z1 and Z2 in FIG. 9 haveirregular boundary that are spread in an angular direction around theedge of the substrate. Accordingly, in an embodiment, the determiningthe zone involves determining a radial boundary and an angular span(e.g., θ1 a and θ1 b of Z1 and θ2 of Z2 in FIG. 9 ) of the radialboundary distribution of the residue based on the variation of thedistribution of the residue exceeding a predefined threshold in theradial direction, an angular direction or a combination thereof.

The method 500, in process P56, involves determining, via the computingsystem (e.g., system 100 of FIG. 14 ), the probabilistic model 544 basedon the zone 542 and the distribution of the residue values or the valuesof the characteristic of the substrate within the zone. Theprobabilistic model 544 is a model configured to predict acharacteristic of a pattern within a particular zone of the substrate,where the zone is defined based on the distribution of the residue asdiscussed earlier. Accordingly, a probabilistic model is defined perzone of the substrate. Thus, in an embodiment, the probabilistic model544 comprises a set of probabilistic models.

In an embodiment, the determining the probabilistic model 544 involvesobtaining (e.g., via a metrology tool) values of the characteristic ofthe pattern of a substrate within the zone (e.g., zones Z1, Z2), anddetermining statistical parameters of the probabilistic model based onvalues of the characteristic of the pattern or values of the residuecorresponding to the characteristic of the pattern within the zone. Inan embodiment, the statistical parameters of the probabilistic modelcomprise a mean and standard deviation (or variance) values. In anembodiment, the probabilistic model is a Gaussian distribution having amean and standard deviation fitted based on the values of thecharacteristic of the pattern within one or more zones. In anembodiment, a statistical parameter may be a measured range of values orhigher moments such as skewness and kurtosis.

In an embodiment, the probabilistic model is adaptive. In other words,one or more parameters of the probabilistic model may be modified basedon the changes in the zone(s) or a number of measurements within a zone.For example, over a period of time, the patterning process may driftresulting in change in spatial characteristic of the substrate. Forexample, more defect may start to appear at a center compared topatterning of previous substrates. Such change in spatial characteristicwill be reflected in the spatial map of the residual, which will affectthe zones (e.g., the boundary of the zone) that are determined based onthe residuals as discussed in process P54. For example, a zone (e.g.,Z1) may increase in size, more discrete regions of the substrate (e.g.,a center portion) may be included in the zone (e.g., Z1), etc. As thezones change, the probabilistic model may be modified based on suchchanged zones.

For example, the method 500, in process P58, further involves adjusting,via the computing system (e.g., system 100 of FIG. 14 ), theprobabilistic model 544, or generating a new model, if a new zone iscreated. The process P58 involves obtaining additional metrology data548 (e.g., from subsequently processed substrates) and distribution ofthe residues corresponding to the additional data, adjusting the zone(e.g., 542) based on the distribution of the residues corresponding tothe additional data, and adjusting the probabilistic model 544 based onan adjusted zone 542′. In an embodiment, the adjusting of theprobabilistic model 544 involves adjusting a statistical parameter ofthe probabilistic model to improve accuracy of measurements of themetrology tool (e.g., e-beam based data or measurements). For example,adjusting a mean and variance of the probabilistic model associated withthe adjusted zone 542′. The adjusting of the zones may be performed in asimilar manner as discussed in process P54, for example, inputting theadditional data to the clustering algorithm and depending on a variation(resulting from the additional data) of the distribution of the residue,a different set of zone may be identified or boundaries of the existingzones 542 may be adjusted.

The method 500, in process P60, may further involve ordering the zonesaccording to the variations in residue and guiding the metrology tool toappropriate zones to collect data. The number of sampling points perzone may be different. For example, relatively high number of sample ordata points (100, 150, 300, etc.) may be obtained from a zone havinghighest variation and only few samples (e.g., 10, 15, 20, etc.) may beobtained from a zone having relatively low variation within the spatialmap.

In an embodiment, process P60 involves ordering the plurality of zonessuch that a zone of the plurality of zones is arranged in a descendingorder based on associated values of the variation of the distribution ofthe residue within the spatial map 501. Further, the determining of thesampling plan is based on the ordering of the plurality of zones and theprobability predicted by the probabilistic model corresponding to agiven zone. In an embodiment, the descending order refers to arrangingzones based on decreasing values of variation of the distribution of theresidue. For example, the descending order comprises a first zoneassociated with a highest value of the variation, a second zoneassociated with a second highest value of the variation, . . . , and thelast zone associated with the lowest value of the variation of thedistribution of the residue.

Further, the method involves guiding a metrology tool (e.g., EBI oroptical tool) to measure a characteristic of a pattern at differentlocations on a printed substrate based on the ordered plurality ofzones. In an embodiment, a pattern (e.g., having a contact hole and aline) at different locations refer to a pattern that may be printed ondifferent locations on a substrate such as within one die or acrossdifferent dies on the same substrate.

Furthermore, the measurements obtained in the process P60 may be used todetermine defects. For example, the method 500 may involve determiningthe characteristics of the pattern on the printed substrate that areoutside a specification based on the measurements from the metrologytool. For example, CD values within a first zone (e.g., Z1) may beobtained and checked whether the CD values breach a predefinedthreshold. If there is a breach, then a defect is detected. According tothe present disclosure, the zone 542 are adjusted based on more databeing collected and further based on the adjusted zones 542′, theprobabilistic model 544 is adjusted. Thus, adjusted probabilistic model544′ can predict the probability of finding a defect where the metrologytool is directly more accurately.

Thus, in an embodiment, the probabilistic model may be used fordetermining, based on a probability determined by the probabilisticmodel 544 (or the adjusted probabilistic model 544′), the predictedpresence of at least one physical item (e.g., a printed substrate) outof specification in a measurement location or field of view of ametrology tool. Further, based on the probability, a sampling plan ofmeasurement locations can be determined that indicates where to measureon physical item instances, if any, that are out of specification.

In an example, the probability (e.g., 623) that a pattern is a defect isthe integration of a PDF of a CD (as an example of an attribute of thedistribution of the characteristic) over a range from minus infinity toa threshold value (e.g., 625 in plot 620 of FIG. 6B). Practicalconsiderations may affect the choice of the threshold value. Forexample, if the total number of inspections or the amount of timeavailable for inspection is limited, the threshold value may be madesmaller, thereby reducing the number of patterns considered defects. Thethreshold value may be normalized using data from a test substrate. Forexample, the threshold value may be chosen such that the totalprobability of defects is comparable to (e.g., within an order ofmagnitude from) the actual number of defects on the test substrate.

The probability that the pattern is a defect may be used to guideinspection of a substrate produced by the device manufacturing process.A pattern with a higher probability of being a defect may be prioritizedin the inspection over a pattern with a lower probability of being adefect.

FIGS. 6A-6D illustrates an example method of obtaining a spatial map 630(an example of 501) of the distribution of a residue 611. According toan embodiment, referring to FIG. 6A, the residue 611 is a histogram of adifference between a verified characteristic of a pattern and apredicted characteristic of a pattern. For example, verified values ofthe characteristic (e.g., CD uniformity (CDU), line width roughness(LWR), line edge roughness (LER), etc.) of pattern instances may beactual values of the characteristic obtained by measuring the patterninstances, for example, using a suitable metrology tool or simulatedvalues of the characteristic using a rigorous model. While a predictvalue of the characteristic of the pattern instances are obtained usingthe non-probabilistic model. In an embodiment, the residue 611 may bedetermined as a difference between verified CD and a predicted CD valuesand plotted on a graph such as graph 610. The residue 611 has adistribution across the substrate as shown. Further, an attribute of thedistribution of the residue 611 may be determined as discussed inprocess P52. For example, the attribute 613 of the distribution of theresidue may be a PDF, CDF or eCDF. In an embodiment, the attribute 613(e.g., PDF) may be interchangeably be used to refer to the residue 611or the distribution of the residue 611.

In an embodiment, referring to residual plot 610, the attribute 613 ofthe distribution of the residue is determined based on simulation dataand measured data corresponding to a characteristic of an ensemble ofphysical items (e.g., N printed substrates having different patterntypes or similar pattern types). As mentioned earlier in method 500, theattribute 613 of the distribution of the residue with respect to theensemble of physical items comprises a cumulative distribution functionfor the ensemble of physical item instances. In an embodiment, theattribute 613 of the distribution of the residue with respect to theensemble involves the attribute of the distribution of the residue withrespect to at least one physical item instance corresponding to at leastone physical item type of the ensemble to the power of a number ofphysical item instances in the ensemble. In an embodiment, the attribute613 of the distribution of the residue with respect to the ensemble is afunction defined at least by [1−(1−eCDF)N] or [1−(1−CDF)N], wherein N isthe number of physical item instances in the ensemble, CDF is acumulative distribution function of the distribution of the residue withrespect to at least one physical item instance corresponding to at leastone physical item type of the ensemble, and eCDF is an empiricalcumulative distribution function of the distribution of the residue withrespect to at least one physical item instance corresponding to at leastone physical item type of the ensemble. In an embodiment, the physicalitem instance corresponds to a pattern on a substrate produced by adevice manufacturing process.

In an embodiment, based on the attribute 613 a defect probability may bedetermined. For example, an area under the curve of the PDF 613 beyond athreshold value 625 of the characteristic is a probability that a defectmay occur. In an embodiment, the threshold value may be a CD value, adifference in measured CD and a predicted CD, or any characteristic ofthe pattern other than CD.

Such attribute (e.g., 613 is a PDF based on CD values) of the residue(e.g., 611) may be determined at a plurality of locations on asubstrate. For example, a CD-based PDF having a mean and variance isavailable at each of the plurality of locations on the substrate.Referring to FIG. 6C, a spatial distribution of each such CD-based PDFmay form a spatial map 630 of the distribution 633 of the residue. In anembodiment, the CD-based PDF may be further used to determine a defectprobability, as mentioned earlier, at each such location of thesubstrate. So, in an embodiment, the spatial map 630 of such defectprobability also referred as a defect map 630 may be obtained. In thespatial map 630, different locations associated with 633 on thesubstrate have different variance. For example, a variance in residuemay be relatively higher at an edge compared to at the center.

In an embodiment, based on the defect map 630, a sampling scheme 640(see FIG. 6D) may be defined. For example, defects having relativelyhigher probability 643 (e.g., highest probability) across the substratemay be sampled, thus more data corresponding to defects occurrence (alsoreferred as hotspots locations) on the substrate is captured therebyimproving a capture rate of the metrology tool. Such measurements may beimportant in controlling various parameters of the patterning process,optimizing the patterning process, making adjustments to the patterningprocess over a period of time, etc. so that the yield of the patterningprocess is improved. However, if the measured data do not capture thedefects, metrology time and resources may be wasted and the adjustmentsto the patterning process may be ineffective. Thus, an accurate samplingscheme used to guide the metrology tool is important.

According to the present disclosure, the sampling scheme such as 643 maybe determined based on the adaptive probabilistic model (e.g., 544discussed in FIG. 5 ) configured to predict a defect probability. Thus,the more accurate an adaptive probabilistic model 544′ is the moreaccurate the sampling scheme 643 will be, thereby improving the yield.As mentioned earlier, a fixed probabilistic model determined based ondata measured on an entire substrate may not be as accurate as theadaptive probabilistic model (e.g., 544). According to an embodiment,based on the zones, different probabilistic models may be available.

FIGS. 8A-8C illustrate an example of standard deviations of thedistribution of the residue 830 (another example of residue 613 or 733)across the substrate in a radial direction and how the distribution ofthe residue 830 and thereby the corresponding attribute of thedistribution changes due to spatial variations across the substrate. Theplot, in FIG. 8A, shows a standard deviation values of the residue 830along a radial direction from a center of a substrate. In an example,the residue 830 is a difference between the computed CD and measured CDvalues corresponding to a pattern on the substrate. As shown, thestandard deviation of the residue 830 is approximately around 4 at thecenter and remains around 4 away from the center along the radialdirection. The standard deviation of the residue 830 does not varysubstantially from 0 (center) to approximately 130 cm radius across thesubstrate. A distribution of residue 852 within such region is shown inplot 850 of FIG. 8B. The plot 850 shows that the spread of the residue852 is primarily concentrated around a zero value and does not has asignificant tail portion. Thus, indicating a probability of defectswithin 0-130 cm is relatively low.

However, at an edge portion (e.g., between beyond 130 cm), the standarddeviation is relatively higher, for example, approximately 5 around 140cm and 6.5 beyond 140 cm. Also, a distribution of residue 862 at theedge region is shown in plot 860 of FIG. 8C. The plot 860 shows that thedistribution of the residue 862 has a relatively wider spread and have asignificant tail portion. Thus, indicating a probability of defectsbeyond 130 cm is relatively high. FIGS. 8B and 8C clearly show there canbe a significant variation in distribution of the residue at differentlocations on the substrate. Thus, according to the present disclosure,the probabilistic model predicting defects is also adapted according tothe change in variation of the residue and corresponding zones. If asingle probabilistic model based on a single distribution of residue isused for an entire substrate to predict defect, then the probabilisticmodel may not accurately predict defects. On the other hand, a firstprobabilistic model based on a first zone (e.g., having the distribution852) and a second probabilistic model based on a second zone (e.g.,having the distribution 862) are used then defect predictions will bemore accurate. Furthermore, the patterning process may cause a change inspatial characteristic over a period of time, thus changing thedistribution of the residue and the corresponding zones. The presentdisclosure also accounts for such changing zone and accordingly theadjusting of the probabilistic model per zone, as discussed in method500.

Example zones determined based on the distribution of the residue (e.g.,as discussed in process P54 of method 500) are illustrated in FIG. 9 . Aspatial map 900 of a distribution of the residue 930 on a substrate isshown. The distribution of the residue 930 has different variations atdifferent locations. For example, some points (e.g., P10, P11, P12 . . .along an edge) may have a highest variation across the substrate, somepoints (e.g., P20, P21, P22 . . . along the edge or away from the edge)have a second variation, which is lower than the highest variation,while some points around the center of the substrate have leastvariation. Based on such variation of the distribution of the residue930, different zones may be determined using different clusteringtechniques, machine learning models for classification of data, or otherappropriate methods. For example, the first zone Z1 in a radialdirection around the edge spanning at two discrete places on thesubstrate. The first zone Z1 is defined by the boundary B1 a spanning anangle θ1 a and B1 b spanning an angle θ1 b. The second zone Z2 is alsodefined around the edge having a boundary B2 and a relatively wider spanof an angle 82. A third zone Z3 is defined around a center of thesubstrate, where the variation of the distribution of the residue isrelatively lower (e.g., lowest) than for Z1 and Z2. The zone Z3 isdefined by a boundary B3 and spans 360°. Note that the boundaries of thezones Z1, Z2, Z3 are flexible (in terms of radius and angle) havingirregular shape (e.g., radial spread). Further, as mentioned earlier,when more data is obtained, the boundaries of the zones Z1, Z2, Z3 maychange, more zones may be included, or a zone may be removed.Accordingly, the probabilistic model per zone is adapted, as discussedin the process P58.

Furthermore, based on the predictions of the probabilistic model perzone, a different sampling plan may be defined per zone. For example, arelatively greater number of measurements (e.g., more than 100 samplepoints) may be obtained in zone Z1, a relatively lower number ofmeasurements may be obtained in zone Z2 (e.g., 30-100 sample points),relatively few measurements (e.g., less than 30 points) may be obtainedin zone Z3. Thus, predictions based on the sampling data is improved,leading to more efficient use of the e-beam tool for verification ofdefects. In an embodiment, an improved sampling may also improve themetrology tool's capture rate, for example, the metrology time andresources are used more efficiently.

FIG. 10 is a flow chart of a method 1000 for determining for a metrologytool, a sampling plan, of a patterning process, according to anembodiment. In the method 1000, the sampling plan is determined based onthe probability of a defect predicted by a probabilistic model (e.g.,544 or 544′) per zone of the substrate. The sampling plan includeslocations at which measurements must be taken to identify a defectivepattern on the substrate. Thus, in an embodiment, the sampling plan maydetermine locations based on probabilities of defects starting fromhighest probability to lowest probability.

The method 1000, in process P102, involves obtaining a probabilisticmodel 1001 corresponding to a zone of a substrate. For example, theprobabilistic model 1001 (an example of 544 or 544′) can be obtainedaccording to the process P56, as discussed in method 500. Theprobabilistic model 1001 may be a first version of the model obtainedbased on data from N number of substrate (e.g., 10 substrates), or anadjusted model obtained based on additional data from subsequentlyproceed substrate (e.g., 11th, 12th, 15th, 20th, etc.). Further, processP104 involves predicting, via a computing system (e.g., processor 104 ofthe system 100), a probability 1004 using the probabilistic model 1001.In an embodiment, the probability 1004 is a probability of defectoccurrence at a particular location on the substrate. In an embodiment,the defect may be defined in terms of a characteristic (e.g., CD, LWR)of the pattern. Accordingly, the probability 1004 may a value of acharacteristic (e.g., CD, LWR) of the pattern to be measured.

Once the probability of a defect at one or more locations of thesubstrate is known, process P106 involves determining, based on theprobability 1004, a sampling plan 1006 comprising measurement locationson a substrate for measurements of a characteristic to determine whetherthe substrate is out of specification. The probability 1004 can be usedfor the various uses such as for statistic process chart creation, forsampling plan creation, etc.

For example, the probability 1004 can be used to create the samplingplan 1006 for measurement by a metrology tool (e.g., shown in FIGS. 12and 13 ) of a substrate. The sampling plan 1006 can be used to identifydefects across the substrate; the identified defects can be used fordevice manufacturing process modification, control, design, etc. Theprobability that a certain measurement location (e.g., field of view(FOV) or image) has an extremum characteristic (e.g., CD) that exceeds acontrol limit (i.e. contains a defect) provides a methodology toprioritize the locations to be inspected with a metrology tool. Forexample, starting from the measurement location with highestprobability, a sampling plan can be defined where locations are addeduntil a desired criteria of capture of defects is achieved (e.g., alevel of capture rate or nuisance rate is achieved or, for example, whenthe sum of probabilities for the sampling locations reaches 80% orhigher, reaches 85% or higher, reaches 90% or higher, reaches 95% orhigher). In this way, an improved (shorter) inspection time may beachieved.

As a more concrete example, in an embodiment, the probability values ofthe measurement locations can be sorted, for example, in order ofincreasing values and then be used to calculate a cumulativeprobability.

In an embodiment, the sampling plan 1006 may change over time as thepatterning process may cause drifts or deviations from normal operatingparameters such as substrate level, optical parameters of a projectionsystem, etc. Thus, in an embodiment, the process P106 (similar toprocess P58 of method 500) involves obtaining, via the metrology tool(e.g., shown in FIGS. 12 and 13 ), additional metrology datacorresponding to subsequently processed substrates and distribution ofthe residues corresponding to the additional data. Then, adjusting agiven zone of the plurality of zones based on the distribution of theresidues corresponding to the additional data. Once the zones areadjusted, the process further involves adjusting the probabilistic modelbased on the adjusted zone. In an embodiment, the adjusting of theprobabilistic model 1001 involves adjusting a statistical parameter ofthe probabilistic model to improve accuracy of measurements. Further,the process involves, adjusting the sampling plan based on theprobability determined by the adjusted probabilistic model.

In an embodiment, the process P106 for determining the sampling plan1006 may involve obtaining a spatial map (e.g., 501, 730) of adistribution of a residue corresponding to a characteristic of a patternon the substrate, obtaining a plurality of zones (e.g., Z1, Z2, Z3,etc.) of the substrate based on the distribution of the residue andbased on a probabilistic model per zone of the plurality of zones.Further, the process P106 involves ordering the plurality of zones suchthat a zone of the plurality of zones is arranged in a descending orderbased on associated values of the variation of the distribution of theresidue within the spatial map 501. In an embodiment, the descendingorder refers to arranging zones based on decreasing values of variationof the distribution of the residue. For example, the descending ordercomprises a first zone associated with a highest value of the variation,a second zone associated with a second highest value of the variation, .. . , and the last zone associated with the lowest value of thevariation of the distribution of the residue. Further, the process P106involves determining the sampling plan 1006 based on the ordering of theplurality of zones and the probability predicted by the probabilisticmodel corresponding to a given zone.

Once, the sampling plan 1006 is obtained, as discussed above, themetrology tool may be instructed or guided to desired locations, forexample, via the computing system 100 sending signal to the metrologytool (e.g., shown in FIGS. 12 and 13 ). For example, process P108involves guiding, based on the sampling plan 1006, the metrology tool tomeasure a characteristic of a pattern at different locations on aprinted substrate produced by the patterning process. In an embodiment,a pattern (e.g., having a contact hole and a line) at differentlocations refer to a pattern that may be printed on different locationson a substrate such as within one die or across different dies on thesame substrate.

FIG. 11 is a flow chart of a method 1100 for determining zones of asubstrate based on a process variability of a patterning process. In anembodiment, a ‘fingerprint’ of process variability (e.g. local CDU) isassociated with specific process step (or tool) based on the process ortool characteristics. A processing ‘fingerprint’ is a spatialdistribution of errors typically caused by one or more certain processsteps. For example, a substrate table may have a warp in a supportsurface which will consistently introduce certain errors at certainlocations on the substrate patterned using that substrate table. So, thesampling locations can provide a user with information that helpsidentify and/or solve a root cause of defects on the substrate. Anassociation between the fingerprint and a defect (or the residue) can beused to quantify process or tool contributions to observed defects.Then, signals (e.g., measurement data) from the processing tool(s) canbe used to adapt a sampling plan in-line (i.e., during manufacturing),based on, for example, machine-learning algorithms linking such signalsto changes in the variability of the hotspots characteristics on printedsubstrates.

The method 1100, in process P112, involves obtaining (i) a spatial map1101 of a distribution of a residue corresponding to a characteristic ofa pattern on a substrate, and (ii) a process variation 1103 of aparameter of the patterning process. In an embodiment, the parameter ofthe patterning process refers to a process variable of the patterningprocess. For example, the parameter is at least one of dose, focus, anoptical parameter, and moving standard deviation of movement (MSDz) ofthe substrate in the normal direction of the substrate, or movingstandard deviation (MSDx,y) of movement of the substrate in a directionparallel to the substrate.

The spatial map 1101 and the process variation 1103 may be related toeach other, where the process variation 1103 may affect the spatial map1101. Thus, the method 1100, in process P114, involves detecting arelationship 1104 between the spatial map 1101 of the distribution ofthe residue and the process variation 1103 of the parameter of thepatterning process.

The method 1100, in process P116, involves determining a zone 1106 (or aplurality of zones 1106) based on the relationship 1104. For example, inan embodiment, the determining the zone involves determining, based onthe relationship, whether the process variation of the parameter of thepatterning process causes a change in the distribution of the residue toexceed a predefined threshold, and responsive to the exceeding of thepredefined threshold, defining a different zone.

The method 1100, in process P118, involves determining, via thecomputing system, the probabilistic model 1108 based on the zone and thedistribution of the residue values or the values of the characteristicof the pattern on the substrate within the zone.

Furthermore, the method 110 may involve process P106 to determine asampling plan based on the zones 1106 and further using the samplingplan to guide the metrology tool (e.g., shown in FIGS. 12 and 13 ), asdiscussed in the process P108.

As mentioned earlier, inspection of, e.g., semiconductor wafers is oftendone with optics-based sub-resolution tools (bright-field inspection).But, in some cases, certain features to be measured are too small to beeffectively measured using bright-field inspection. For example,bright-field inspection of defects in features of a semiconductor devicecan be challenging. Moreover, as time progresses, features that arebeing made using patterning processes (e.g., semiconductor features madeusing lithography) are becoming smaller and in many cases, the densityof features is also increasing. Accordingly, a higher resolutioninspection technique is used and desired. An example inspectiontechnique is electron beam inspection. Electron beam inspection involvesfocusing a beam of electrons on a small spot on the substrate to beinspected. An image is formed by providing relative movement between thebeam and the substrate (hereinafter referred to as scanning the electronbeam) over the area of the substrate inspected and collecting secondaryand/or backscattered electrons with an electron detector. The image datais then processed to, for example, identify defects.

So, in an embodiment, the inspection apparatus may be an electron beaminspection apparatus (e.g., the same as or similar to a scanningelectron microscope (SEM)) that yields an image of a structure (e.g.,some or all the structure of a device, such as an integrated circuit)exposed or transferred on the substrate.

The probability that one or more pattern instances are a defect may beused for various purposes. For example, the probabilities can be used toderive a statistical defect count per substrate that should be close tothe actual number of defects actually present on any given substrate. Inan embodiment, a statistical process chart can be created based on thisstatistical defect count. This also allows a decision to be made aboutfurther processing of the substrate(s) analyzed using this probabilisticcomputational method with, e.g., a rapid turn-around time.

The probabilities and/or statistical defect count can be used toprioritize locations to be inspected with a metrology tool (such as anelectron beam inspection tool shown in FIGS. 12 and 13 ). Based on theprobabilities and/or statistical defect count, a sampling scheme can bedefined where locations are added to the sampling scheme until, e.g., adesired level of capture rate is achieved (e.g., when the sum ofprobabilities for the sampling sites reaches 90%) or a desired level ofnuisance rate is achieved. A capture rate can be defined as the numberof true positive defects divided by the total of the true positivedefects and the false negative defects. The nuisance rate can be definedas the number of false positive defects divided by the total of the truepositive defects and the false positive defects. As a result, animproved (shorter) inspection time may be achieved. As a relatedbenefit, the full set of sampling locations identified in such a wayshould provide a spatial signature on the substrate analyzed with theprobabilistic computational method of the predicted defects, which cancorrelate with or improve a correlation with, a processing ‘fingerprint’of one or more certain process steps as part of the device manufacturingmethod.

The probability that the pattern is a defect may be used to guideinspection of a substrate produced by the device manufacturing process.A pattern instance with a higher probability of being a defect may beprioritized in the inspection over a pattern instance with a lowerprobability of being a defect.

In an embodiment, the number of pattern instances to be inspected (orthe measurement locations where those pattern instances are located) perpattern type or set of a particular plurality of pattern types can bedetermined based on the statistical expectation of number of defects foreach such pattern type or set of a particular plurality of patterntypes. In an embodiment, for each pattern type or set of a particularplurality of pattern types, the inspection location can be determinebased on, for example, (i) probability of a defect, and (ii) a spatialdistribution of the associated pattern instance on the substrate so to,e.g., maximize the benefit of a measurement spot, FOV, or image obtainedby a metrology tool (e.g., shown in FIGS. 12 and 13 ). In an embodiment,a fixed fraction of inspection time can be assigned to uniform samplingand measuring certain anchor features.

In an example, an ordered list of patterns may be generated based on aplurality of zones, as discussed earlier in methods 500 and 1000. Theordered list includes those pattern instances with the highestprobabilities of being defects (e.g., determined using the probabilisticmodel 544 or the adjusted probabilistic model 548); in other words, theordered list comprises a subset of pattern instances among the set ofpattern instances, where the pattern instances in the subset have higherprobabilities of being defects than the pattern instances in the set butnot in the subset. The number of pattern instances in the ordered listmay be determined by the inspection throughput or may be empiricallydetermined. The number of pattern instances in the ordered list may belimited by the amount of time before the next substrate for inspectionarrives. The number of pattern instances in the ordered list may belimited by the amount of radiation the substrate is allowed to receiveduring the inspection. In an example, the order of the pattern instancesin the ordered list may be a descending order of the probabilities. Inother words, the order may be that a pattern instance with higherprobability of being a defect is inspected before a pattern instancewith a lower probability of being a defect (“the order of descendingprobabilities”). In an example, the order of the pattern instances inthe ordered list may be an order that causes a cost function to be at anextremum. In an embodiment, the cost function is a function of the orderof the pattern instances and may represent the probabilities, theamounts of time needed for inspecting the pattern instances, thedistance from one pattern instance to the next pattern instance, and/orother indicators of the performance of the inspection.

FIG. 12 schematically depicts an embodiment of an electron beaminspection apparatus 200. A primary electron beam 202 emitted from anelectron source 201 is converged by condenser lens 203 and then passesthrough a beam deflector 204, an E×B deflector 205, and an objectivelens 206 to irradiate a substrate 100 on a substrate table 101 at afocus.

When the substrate 100 is irradiated with electron beam 202, secondaryelectrons are generated from the substrate 100. The secondary electronsare deflected by the E×B deflector 205 and detected by a secondaryelectron detector 207. A two-dimensional electron beam image can beobtained by detecting the electrons generated from the sample insynchronization with, e.g., two dimensional scanning of the electronbeam by beam deflector 204 or with repetitive scanning of electron beam202 by beam deflector 204 in an X or Y direction, together withcontinuous movement of the substrate 100 by the substrate table 101 inthe other of the X or Y direction. Thus, in an embodiment, the electronbeam inspection apparatus has a field of view for the electron beamdefined by the angular range into which the electron beam can beprovided by the electron beam inspection apparatus (e.g., the angularrange through which the deflector 204 can provide the electron beam202). Thus, the spatial extent of the field of the view is the spatialextent to which the angular range of the electron beam can impinge on asurface (wherein the surface can be stationary or can move with respectto the field).

A signal detected by secondary electron detector 207 is converted to adigital signal by an analog/digital (ND) converter 208, and the digitalsignal is sent to an image processing system 300. In an embodiment, theimage processing system 300 may have memory 303 to store all or part ofdigital images for processing by a processing unit 304. The processingunit 304 (e.g., specially designed hardware or a combination of hardwareand software or a computer readable medium comprising software) isconfigured to convert or process the digital images into datasetsrepresentative of the digital images. In an embodiment, the processingunit 304 is configured or programmed to cause execution of a methoddescribed herein. Further, image processing system 300 may have astorage medium 301 configured to store the digital images andcorresponding datasets in a reference database. A display device 302 maybe connected with the image processing system 300, so that an operatorcan conduct necessary operation of the equipment with the help of agraphical user interface.

FIG. 13 schematically illustrates a further embodiment of an inspectionapparatus. The system is used to inspect a sample 90 (such as asubstrate) on a sample stage 89 and comprises a charged particle beamgenerator 81, a condenser lens module 82, a probe forming objective lensmodule 83, a charged particle beam deflection module 84, a secondarycharged particle detector module 85, and an image forming module 86.

The charged particle beam generator 81 generates a primary chargedparticle beam 91. The condenser lens module 82 condenses the generatedprimary charged particle beam 91. The probe forming objective lensmodule 83 focuses the condensed primary charged particle beam into acharged particle beam probe 92. The charged particle beam deflectionmodule 84 scans the formed charged particle beam probe 92 across thesurface of an area of interest on the sample 90 secured on the samplestage 89. In an embodiment, the charged particle beam generator 81, thecondenser lens module 82 and the probe forming objective lens module 83,or their equivalent designs, alternatives or any combination thereof,together form a charged particle beam probe generator which generatesthe scanning charged particle beam probe 92.

The secondary charged particle detector module 85 detects secondarycharged particles 93 emitted from the sample surface (maybe also alongwith other reflected or scattered charged particles from the samplesurface) upon being bombarded by the charged particle beam probe 92 togenerate a secondary charged particle detection signal 94. The imageforming module 86 (e.g., a computing device) is coupled with thesecondary charged particle detector module 85 to receive the secondarycharged particle detection signal 94 from the secondary charged particledetector module 85 and accordingly forming at least one scanned image.In an embodiment, the secondary charged particle detector module 85 andimage forming module 86, or their equivalent designs, alternatives orany combination thereof, together form an image forming apparatus whichforms a scanned image from detected secondary charged particles emittedfrom sample 90 being bombarded by the charged particle beam probe 92.

In an embodiment, a monitoring module 87 is coupled to the image formingmodule 86 of the image forming apparatus to monitor, control, etc. thepatterning process and/or derive a parameter for patterning processdesign, control, monitoring, etc. using the scanned image of the sample90 received from image forming module 86. So, in an embodiment, themonitoring module 87 is configured or programmed to cause execution of amethod described herein. In an embodiment, the monitoring module 87comprises a computing device. In an embodiment, the monitoring module 87comprises a computer program to provide functionality herein and encodedon a computer readable medium forming, or disposed within, themonitoring module 87.

In an embodiment, like the electron beam inspection tool of FIG. 12 thatuses a probe to inspect a substrate, the electron current in the systemof FIG. 13 is significantly larger compared to, e.g., a CD SEM such asdepicted in FIG. 12 , such that the probe spot is large enough so thatthe inspection speed can be fast. However, the resolution may not be ashigh as compared to a CD SEM because of the large probe spot. In anembodiment, the above discussed inspection apparatus (in FIG. 13 or 14 )may be single beam or a multi-beam apparatus without limiting the scopeof the present disclosure.

The SEM images, from, e.g., the system of FIG. 12 and/or FIG. 13 , maybe processed to extract contours that describe the edges of objects,representing device structures, in the image. These contours are thentypically quantified via metrics, such as CD, at user-defined cut-lines.Thus, typically, the images of device structures are compared andquantified via metrics, such as an edge-to-edge distance (CD) measuredon extracted contours or simple pixel differences between images.

FIG. 14 is a block diagram that illustrates a computing system 100 whichcan assist in implementing the optimization methods and flows disclosedherein. Computing system 100 may comprise one or more individualcomputer systems, such as computer system 101. Further, computing system100 may comprise, for example, a metrology tool or a portion of ametrology tool. Computer system 101 includes a bus 102 or othercommunication mechanism for communicating information, and a processor104 (or multiple processors 104 and 105) coupled with bus 102 forprocessing information. Computer system 101 also includes a main memory106, such as a random access memory (RAM) or other dynamic storagedevice, coupled to bus 102 for storing information and instructions tobe executed by processor 104. Main memory 106 also may be used forstoring temporary variables or other intermediate information duringexecution of instructions to be executed by processor 104. Computersystem 101 further includes a read only memory (ROM) 108 or other staticstorage device coupled to bus 102 for storing static information andinstructions for processor 104. A storage device 110, such as a magneticdisk or optical disk, is provided and coupled to bus 102 for storinginformation and instructions.

Computer system 101 may be coupled via bus 102 to a display 112, such asa cathode ray tube (CRT) or flat panel or touch panel display fordisplaying information to a computer user. An input device 114,including alphanumeric and other keys, is coupled to bus 102 forcommunicating information and command selections to processor 104.Another type of user input device is cursor control 116, such as amouse, a trackball, or cursor direction keys for communicating directioninformation and command selections to processor 104 and for controllingcursor movement on display 112. This input device typically has twodegrees of freedom in two axes, a first axis (e.g., x) and a second axis(e.g., y), that allows the device to specify positions in a plane. Atouch panel (screen) display may also be used as an input device.

According to one embodiment, portions of a process described herein maybe performed by computer system 101 in response to processor 104executing one or more sequences of one or more instructions contained inmain memory 106. Such instructions may be read into main memory 106 fromanother computer-readable medium, such as storage device 110. Executionof the sequences of instructions contained in main memory 106 causesprocessor 104 to perform the process steps described herein. One or moreprocessors in a multi-processing arrangement may also be employed toexecute the sequences of instructions contained in main memory 106. Inalternative embodiments, hard-wired circuitry may be used in place of orin combination with software instructions. Thus, embodiments are notlimited to any specific combination of hardware circuitry and software.

The term “computer-readable medium” as used herein refers to any mediumthat participates in providing instructions to processor 104 forexecution. Such a medium may take many forms, including but not limitedto, non-volatile media, volatile media, and transmission media.Non-volatile media include, for example, optical or magnetic disks, suchas storage device 110. Volatile media include dynamic memory, such asmain memory 106. Transmission media include coaxial cables, copper wireand fiber optics, including the wires that comprise bus 102.Transmission media can also take the form of acoustic or light waves,such as those generated during radio frequency (RF) and infrared (IR)data communications. Common forms of computer-readable media include,for example, a floppy disk, a flexible disk, hard disk, magnetic tape,any other magnetic medium, a CD-ROM, DVD, any other optical medium,punch cards, paper tape, any other physical medium with patterns ofholes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip orcartridge, a carrier wave as described hereinafter, or any other mediumfrom which a computer can read.

Various forms of computer readable media may be involved in carrying oneor more sequences of one or more instructions to processor 104 forexecution. For example, the instructions may initially be borne on amagnetic disk of a remote computer. The remote computer can load theinstructions into its dynamic memory and send the instructions over atelephone line using a modem. A modem local to computer system 101 canreceive the data on the telephone line and use an infrared transmitterto convert the data to an infrared signal. An infrared detector coupledto bus 102 can receive the data carried in the infrared signal and placethe data on bus 102. Bus 102 carries the data to main memory 106, fromwhich processor 104 retrieves and executes the instructions. Theinstructions received by main memory 106 may optionally be stored onstorage device 110 either before or after execution by processor 104.

Computer system 101 may also include a communication interface 118coupled to bus 102. Communication interface 118 provides a two-way datacommunication coupling to a network link 120 that is connected to alocal network 122. For example, communication interface 118 may be anintegrated services digital network (ISDN) card or a modem to provide adata communication connection to a corresponding type of telephone line.As another example, communication interface 118 may be a local areanetwork (LAN) card to provide a data communication connection to acompatible LAN. Wireless links may also be implemented. In any suchimplementation, communication interface 118 sends and receiveselectrical, electromagnetic or optical signals that carry digital datastreams representing various types of information.

Network link 120 typically provides data communication through one ormore networks to other data devices. For example, network link 120 mayprovide a connection through local network 122 to a host computer 124 orto data equipment operated by an Internet Service Provider (ISP) 126.ISP 126 in turn provides data communication services through theworldwide packet data communication network, now commonly referred to asthe “Internet” 128. Local network 122 and Internet 128 both useelectrical, electromagnetic or optical signals that carry digital datastreams. The signals through the various networks and the signals onnetwork link 120 and through communication interface 118, which carrythe digital data to and from computer system 101, are exemplary forms ofcarrier waves transporting the information. Communication between theone or more computer system 101 s that comprise computing system 100 mayoccur via any of various mediums. For example, communication between theone or more computer system 101 s can occur via local network 122,internet 128, a wi-fi network, a cellular network, or any other usablecommunications medium.

Computer system 101 can send messages and receive data, includingprogram code, through the network(s), network link 120, andcommunication interface 118. In the Internet example, a server 130 mighttransmit a requested code for an application program through Internet128, ISP 126, local network 122 and communication interface 118. Inaccordance with one or more embodiments, one such downloaded applicationprovides for the illumination optimization of the embodiment, forexample. The received code may be executed by processor 104 as it isreceived, or stored in storage device 110, or other non-volatile storagefor later execution. In this manner, computer system 101 may obtainapplication code in the form of a carrier wave.

FIG. 15 schematically depicts another exemplary lithographic projectionapparatus LA that includes:

-   -   a source collector module SO to provide radiation.    -   an illumination system (illuminator) IL configured to condition        a radiation beam B (e.g. EUV radiation) from the source        collector module SO.    -   a support structure (e.g. a mask table) MT constructed to        support a patterning device (e.g. a mask or a reticle) MA and        connected to a first positioner PM configured to accurately        position the patterning device;    -   a substrate table (e.g. a wafer table) WT constructed to hold a        substrate (e.g. a resist coated wafer) W and connected to a        second positioner PW configured to accurately position the        substrate; and    -   a projection system (e.g. a reflective projection system) PS        configured to project a pattern imparted to the radiation beam B        by patterning device MA onto a target portion C (e.g. comprising        one or more dies) of the substrate W.

As here depicted, the apparatus LA is of a reflective type (e.g.employing a reflective mask). It is to be noted that because mostmaterials are absorptive within the EUV wavelength range, the patterningdevice may have multilayer reflectors comprising, for example, amulti-layer stack of molybdenum and silicon. In one example, themulti-stack reflector has a 40 layer pairs of Molybdenum and Siliconwhere the thickness of each layer is a quarter wavelength. Even smallerwavelengths may be produced with X-ray lithography. Since most materialis absorptive at EUV and x-ray wavelengths, a thin piece of patternedabsorbing material on the patterning device topography (e.g., a TaNabsorber on top of the multi-layer reflector) defines where featureswould print (positive resist) or not print (negative resist).

Referring to FIG. 15 , the illuminator IL receives an extreme ultraviolet radiation beam from the source collector module SO. Methods toproduce EUV radiation include, but are not necessarily limited to,converting a material into a plasma state that has at least one element,e.g., xenon, lithium or tin, with one or more emission lines in the EUVrange. In one such method, often termed laser produced plasma (“LPP”)the plasma can be produced by irradiating a fuel, such as a droplet,stream or cluster of material having the line-emitting element, with alaser beam. The source collector module SO may be part of an EUVradiation system including a laser, not shown in FIG. 15 , for providingthe laser beam exciting the fuel. The resulting plasma emits outputradiation, e.g., EUV radiation, which is collected using a radiationcollector, disposed in the source collector module. The laser and thesource collector module may be separate entities, for example when a CO2laser is used to provide the laser beam for fuel excitation.

In such cases, the laser is not considered to form part of thelithographic apparatus and the radiation beam is passed from the laserto the source collector module with the aid of a beam delivery systemcomprising, for example, suitable directing mirrors or a beam expander.In other cases the radiation source may be an integral part of thesource collector module, for example when the radiation source is adischarge produced plasma EUV generator, often termed as a DPP radiationsource.

The illuminator IL may comprise an adjuster for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter or inner radial extent (commonly referred to as σ-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator IL maycomprise various other components, such as facetted field and pupilmirror devices. The illuminator may be used to condition the radiationbeam, to have a desired uniformity and intensity distribution in itscross section.

The radiation beam B is incident on the patterning device (e.g., mask)MA, which is held on the support structure (e.g., mask table) MT, and ispatterned by the patterning device. After being reflected from thepatterning device (e.g. mask) MA, the radiation beam B passes throughthe projection system PS, which focuses the beam onto a target portion Cof the substrate W. With the aid of the second positioner PW andposition sensor PS2 (e.g. an interferometric device, linear encoder orcapacitive sensor), the substrate table WT can be moved accurately, e.g.so as to position different target portions C in the path of theradiation beam B. Similarly, the first positioner PM and anotherposition sensor PS1 can be used to accurately position the patterningdevice (e.g. mask) MA with respect to the path of the radiation beam B.Patterning device (e.g. mask) MA and substrate W may be aligned usingpatterning device alignment marks M1, M2 and substrate alignment marksP1, P2.

The depicted apparatus LA could be used in at least one of the followingmodes:

1. In step mode, the support structure (e.g. mask table) MT and thesubstrate table WT are kept essentially stationary, while an entirepattern imparted to the radiation beam is projected onto a targetportion C at one time (i.e. a single static exposure). The substratetable WT is then shifted in the X or Y direction so that a differenttarget portion C can be exposed.

2. In scan mode, the support structure (e.g. mask table) MT and thesubstrate table WT are scanned synchronously while a pattern imparted tothe radiation beam is projected onto a target portion C (i.e. a singledynamic exposure). The velocity and direction of the substrate table WTrelative to the support structure (e.g. mask table) MT may be determinedby the (de-)magnification and image reversal characteristics of theprojection system PS.

3. In another mode, the support structure (e.g. mask table) MT is keptessentially stationary holding a programmable patterning device, and thesubstrate table WT is moved or scanned while a pattern imparted to theradiation beam is projected onto a target portion C. In this mode,generally a pulsed radiation source is employed and the programmablepatterning device is updated as required after each movement of thesubstrate table WT or in between successive radiation pulses during ascan. This mode of operation can be readily applied to masklesslithography that utilizes programmable patterning device, such as aprogrammable mirror array of a type as referred to above.

FIG. 16 shows the apparatus LA in more detail, including the sourcecollector module SO, the illumination system IL, and the projectionsystem PS. The source collector module SO is constructed and arrangedsuch that a vacuum environment can be maintained in an enclosingstructure 220 of the source collector module SO. An EUV radiationemitting plasma 210 may be formed by a discharge produced plasmaradiation source. EUV radiation may be produced by a gas or vapor, forexample Xe gas, Li vapor or Sn vapor in which the very hot plasma 210 iscreated to emit radiation in the EUV range of the electromagneticspectrum. The very hot plasma 210 is created by, for example, anelectrical discharge causing an at least partially ionized plasma.Partial pressures of, for example, 10 Pa of Xe, Li, Sn vapor or anyother suitable gas or vapor may be required for efficient generation ofthe radiation. In an embodiment, a plasma of excited tin (Sn) isprovided to produce EUV radiation.

The radiation emitted by the hot plasma 210 is passed from a sourcechamber 211 into a collector chamber 212 via an optional gas barrier orcontaminant trap 230 (in some cases also referred to as contaminantbarrier or foil trap) which is positioned in or behind an opening insource chamber 211. The contaminant trap 230 may include a channelstructure. Contamination trap 230 may also include a gas barrier or acombination of a gas barrier and a channel structure. The contaminanttrap or contaminant barrier 230 further indicated herein at leastincludes a channel structure, as known in the art.

The collector chamber 211 may include a radiation collector CO which maybe a so-called grazing incidence collector. Radiation collector CO hasan upstream radiation collector side 251 and a downstream radiationcollector side 252. Radiation that traverses collector CO can bereflected off a grating spectral filter 240 to be focused in a virtualsource point IF along the optical axis indicated by the dot-dashed line‘0’. The virtual source point IF is commonly referred to as theintermediate focus, and the source collector module is arranged suchthat the intermediate focus IF is located at or near an opening 221 inthe enclosing structure 220. The virtual source point IF is an image ofthe radiation emitting plasma 210.

Subsequently the radiation traverses the illumination system IL, whichmay include a facetted field mirror device 22 and a facetted pupilmirror device 24 arranged to provide a desired angular distribution ofthe radiation beam 21, at the patterning device MA, as well as a desireduniformity of radiation intensity at the patterning device MA. Uponreflection of the beam of radiation 21 at the patterning device MA, heldby the support structure MT, a patterned beam 26 is formed and thepatterned beam 26 is imaged by the projection system PS via reflectiveelements 28, 30 onto a substrate W held by the substrate table WT.

More elements than shown may generally be present in illumination opticsunit IL and projection system PS. The grating spectral filter 240 mayoptionally be present, depending upon the type of lithographicapparatus. Further, there may be more mirrors present than those shownin the Figures, for example there may be 1-6 additional reflectiveelements present in the projection system PS than shown in FIG. 16 .

Collector optic CO, as illustrated in FIG. 16 , is depicted as a nestedcollector with grazing incidence reflectors 253, 254 and 255, just as anexample of a collector (or collector mirror). The grazing incidencereflectors 253, 254 and 255 are disposed axially symmetric around theoptical axis O and a collector optic CO of this type is desirably usedin combination with a discharge produced plasma radiation source.

Alternatively, the source collector module SO may be part of an LPPradiation system as shown in FIG. 17 . A laser LAS is arranged todeposit laser energy into a fuel, such as xenon (Xe), tin (Sn) orlithium (Li), creating the highly ionized plasma 210 with electrontemperatures of several 10's of eV. The energetic radiation generatedduring de-excitation and recombination of these ions is emitted from theplasma, collected by a near normal incidence collector optic CO andfocused onto the opening 221 in the enclosing structure 220.

The embodiments may further be described using the following clauses:

1. A method for determining a probabilistic model configured to predicta characteristic of a pattern on a substrate subjected to a patterningprocess, the method comprising:

obtaining a spatial map of a distribution of a residue corresponding tothe characteristic of the pattern on the substrate;

determining, via a computing system, a zone of the spatial map based ona variation of the distribution of the residue within the spatial map;and

determining, via the computing system, the probabilistic model based onthe zone and the distribution of the residue values or the values of thecharacteristic of the pattern on the substrate within the zone.

2. The method of clause 1, wherein the determining the zone comprises:

determining whether the variation of the distribution of the residueexceeds a predefined threshold; and

-   -   responsive to the exceeding of the predefined threshold,        defining a different zone.        3. The method of clause 1 or clause 2, wherein the determining        the zone is an iterative process, wherein a plurality of zones        are obtained based on the variation of the distribution of the        residue, such that a first zone of the plurality of zones has a        first variation of the distribution of the residue, and a second        zone of the plurality of zones has a second variation of the        distribution of the residue.        4. The method of clause 3, wherein an iteration of the        determining the zone comprises:

executing a classification algorithm with the spatial map of thedistribution of the residue as input, the classification algorithmproviding one or more groups of the residue based on the variation inresidue; and

identifying a boundary around each group of the one or more groups ofresidue, wherein the zone is a region within the boundary.

5. The method of clause 3 or clause 4, wherein the iteration of thedetermining the zone further comprises:

obtaining, via a metrology tool, metrology data in the first zone andthe second zone corresponding to the characteristic of the pattern onthe substrate, wherein the first zone and the second zone are separatedby a first boundary between the first zone and the second zone, and thesecond zone is identified by a second boundary; and

modifying the first boundary around the first zone of the residue basedon the metrology data.

6. The method of clause 4, wherein the classification algorithm is amachine learning model trained to identify zones based on the variationof the distribution of the residue or the variation of thecharacteristic of the pattern on the printed substrate.

7. The method of any of clauses 4 to 6, wherein the classificationalgorithm involves a clustering analysis based on at least one of:

k-nearest mean;

mean-shifting;

naive-Bayes and back propagation neural network;

Density-Based Spatial Clustering of Applications with Noise;

Gaussian mixture model; or

hierarchical clustering.

8. The method of any of clauses 1 to 7, wherein the determining the zonecomprises:

determining a radial boundary and an angular span of the radial boundarybased on the variation of the distribution of the residue exceeding apredefined threshold in the radial direction, an angular direction or acombination thereof.

9. The method of any of clauses 1 to 8, wherein the zone is defined interms of radial distance from a center of the substrate.

10. The method of any of clauses 1 to 9, wherein the zone comprises anirregular closed boundary in a radial direction and spanning a certainangular region of the substrate.

11. The method of clauses 1 to 10, wherein the determining theprobabilistic model comprises:

obtaining values of the characteristic of the pattern on the substratewithin the zone; and

determining statistical parameters of the probabilistic model based onvalues of the characteristic of the pattern or values of the residuecorresponding to the characteristic of the pattern within the zone.

12. The method of clause 10, wherein the statistical parameters of theprobabilistic model comprise a mean and standard deviation values.

13. The method of clause 11 or clause 12, wherein the probabilisticmodel is a Gaussian distribution.

14. The method of any of clauses 1 to 13, further comprising:

obtaining, via a metrology tool, additional metrology data correspondingto subsequently processed substrates and distribution of the residuescorresponding to the additional data;

adjusting, via the computing system, the zone based on the distributionof the residues corresponding to the additional data; and

adjusting, via the computing system, the probabilistic model based onthe adjusted zone.

15. The method of clause 14, wherein the adjusting of the probabilisticmodel comprises adjusting a statistical parameter of the probabilisticmodel to improve accuracy of measurements.

16. The method of any of clauses 3 to 15, further comprising:

ordering, via the computing system, the plurality of zones from ahighest value to a lowest value of the variation of the distribution ofthe residue within the spatial map; and

guiding, via the computing system, the metrology tool to measure thecharacteristic of a pattern at different locations on a printedsubstrate based on the ordered plurality of zones.

17. The method of any of clauses 1 to 15, further comprising:

determining, via the computing system, the characteristics of thepattern on the printed substrate that are outside a specification basedon the measurements from the metrology tool.

18. The method of any of clauses 1 to 17, wherein the characteristic isone or more selected from: a position relative to a substrate, aposition relative to one or more other physical item instances, ageometric size, a geometric shape, a measure of a stochastic effect,and/or any combination selected therefrom.19. The method of any of clauses 1 to 18, further comprising:

determining, via the computing system, an attribute of the distributionof the residue based on simulation data and measured data correspondingto the characteristic of an ensemble of physical items.

20. The method of clause 19, wherein the attribute of the distributionof the residue with respect to the ensemble of physical items comprisesa cumulative distribution function for the ensemble of physical iteminstances.

21. The method of any of clauses 18 to 20, wherein the physical iteminstance corresponds to a pattern instance on a substrate produced by adevice manufacturing process.

22. The method of any of clauses 18 to 21, further comprising:

determining, based on the probability determined by probabilistic model,or the adjusted probabilistic model, the predicted presence of at leastone physical item instance out of specification in a measurementlocation or field of view of a metrology tool.

23. The method of any of clauses 1 to 22, further comprising:

determining, based on the probability determined by probabilistic model,or the adjusted probabilistic model, a sampling plan comprisingmeasurement locations on a substrate for measurements of acharacteristic to determine physical item instances, if any, that areout of specification.

24. A method for determining, for a metrology tool, a sampling plan of apatterning process, the method comprising:

obtaining a probabilistic model corresponding to a zone of a substrate;

predicting, via a computing system, a probability using theprobabilistic model; and

determining, via the computing system, based on the probability, asampling plan comprising measurement locations on the substrate formeasurements of a characteristic to determine whether the substrate isout of specification.

25. The method of clause 24, further comprising:

obtaining a spatial map of a distribution of a residue corresponding toa characteristic of a pattern on the substrate;

obtaining a plurality of zones of the substrate based on thedistribution of the residue and based on a probabilistic model per zoneof the plurality of zones; and

ordering, via the computing system, the plurality of zones such that azone of the plurality of zones is arranged in a descending order basedon associated values of the variation of the distribution of the residuewithin the spatial map,

wherein the determining of the sampling plan is based on the ordering ofthe plurality of zones and the probability predicted by theprobabilistic model corresponding to a given zone.

26. The method of clause 24 or clause 25, further comprising:

guiding, based on the sampling plan, the metrology tool to measure acharacteristic of a pattern at different locations on the substrateproduced by the patterning process.

27. The method of clause 25 or clause 26, wherein the determining thesampling plan comprises:

obtaining, via the metrology tool, additional metrology datacorresponding to subsequently processed substrates and distribution ofthe residues corresponding to the additional data;

adjusting, via the computing system, a given zone of the plurality ofzones based on the distribution of the residues corresponding to theadditional data;

adjusting, via the computing system, the probabilistic model based onthe adjusted zone; and

adjusting, via the computing system, the sampling plan based on aprobability determined based on the adjusted probabilistic model.

28. The method of clause 27, wherein the adjusting of the probabilisticmodel comprises adjusting a statistical parameter of the probabilisticmodel to improve accuracy of measurements.

29. A method for determining zones of a substrate based on processvariability of a patterning process, the method comprising:

obtaining (i) a spatial map of a distribution of a residue correspondingto a characteristic of a pattern on a substrate, and (ii) a processvariation of a parameter of the patterning process;

detecting, via a computing system, a relationship between the spatialmap of the distribution of the residue and the process variation of theparameter of the patterning process;

determining, via the computing system, a zone based on the relationship;and determining, via the computing system, the probabilistic model basedon the zone and the distribution of the residue values or the values ofthe characteristic of the pattern on the substrate within the zone.

30. The method of clause 29, wherein the determining the zone comprises:

determining, based on the relationship, whether the process variation ofthe parameter of the patterning process causes a change in thedistribution of the residue to exceed a predefined threshold; and

-   -   responsive to the exceeding of the predefined threshold,        defining a different zone.        31. The method of clause 30, wherein the parameter of the        patterning process is at least one of dose, focus, an optical        parameter, or moving standard deviation of movement of the        substrate.        32. A computer program product comprising a non-transitory        computer readable medium having instructions recorded thereon,        the instructions when executed by a computer system implementing        the method of any of clauses 1 to 31.

The concepts disclosed herein may simulate or mathematically model anygeneric imaging system for imaging sub wavelength features, and may beespecially useful with emerging imaging technologies capable ofproducing wavelengths of an increasingly smaller size. Emergingtechnologies already in use include EUV (extreme ultra violet)lithography that is capable of producing a 193 nm wavelength with theuse of an ArF laser, and even a 157 nm wavelength with the use of aFluorine laser. Moreover, EUV lithography is capable of producingwavelengths within a range of 20-5 nm by using a synchrotron or byhitting a material (either solid or a plasma) with high energy electronsin order to produce photons within this range.

While the concepts disclosed herein may be used for imaging on asubstrate such as a silicon wafer, it shall be understood that thedisclosed concepts may be used with any type of lithographic imagingsystems, e.g., those used for imaging on substrates other than siliconwafers.

Although specific reference may be made in this text to the use ofembodiments in the manufacture of ICs, it should be understood that theembodiments herein may have many other possible applications. Forexample, it may be employed in the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,liquid-crystal displays (LCDs), thin film magnetic heads,micromechanical systems (MEMs), etc. The skilled artisan will appreciatethat, in the context of such alternative applications, any use of theterms “reticle”, “wafer” or “die” herein may be considered as synonymousor interchangeable with the more general terms “patterning device”,“substrate” or “target portion”, respectively. The substrate referred toherein may be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist) or a metrology or inspection tool.Where applicable, the disclosure herein may be applied to such and othersubstrate processing tools. Further, the substrate may be processed morethan once, for example in order to create, for example, a multi-layerIC, so that the term substrate used herein may also refer to a substratethat already contains multiple processed layers.

In the present document, the terms “radiation” and “beam” as used hereinencompass all types of electromagnetic radiation, including ultravioletradiation (e.g. with a wavelength of about 365, about 248, about 193,about 157 or about 126 nm) and extreme ultra-violet (EUV) radiation(e.g. having a wavelength in the range of 5-20 nm), as well as particlebeams, such as ion beams or electron beams.

The terms “optimizing” and “optimization” as used herein refers to ormeans adjusting a patterning apparatus (e.g., a lithography apparatus),a patterning process, etc. such that results or processes have moredesirable characteristics, such as higher accuracy of projection of adesign pattern on a substrate, a larger process window, etc. Thus, theterm “optimizing” and “optimization” as used herein refers to or means aprocess that identifies one or more values for one or more parametersthat provide an improvement, e.g. a local optimum, in at least onerelevant metric, compared to an initial set of one or more values forthose one or more parameters. “Optimum” and other related terms shouldbe construed accordingly. In an embodiment, optimization steps can beapplied iteratively to provide further improvements in one or moremetrics.

Aspects of the invention can be implemented in any convenient form. Forexample, an embodiment may be implemented by one or more appropriatecomputer programs which may be carried on an appropriate carrier mediumwhich may be a tangible carrier medium (e.g. a disk) or an intangiblecarrier medium (e.g. a communications signal). Embodiments of theinvention may be implemented using suitable apparatus which mayspecifically take the form of a programmable computer running a computerprogram arranged to implement a method as described herein. Thus,embodiments of the disclosure may be implemented in hardware, firmware,software, or any combination thereof. Embodiments of the disclosure mayalso be implemented as instructions stored on a machine-readable medium,which may be read and executed by one or more processors. Amachine-readable medium may include any mechanism for storing ortransmitting information in a form readable by a machine (e.g., acomputing device). For example, a machine-readable medium may includeread only memory (ROM); random access memory (RAM); magnetic diskstorage media; optical storage media; flash memory devices; electrical,optical, acoustical or other forms of propagated signals (e.g. carrierwaves, infrared signals, digital signals, etc.), and others. Further,firmware, software, routines, instructions may be described herein asperforming certain actions. However, it should be appreciated that suchdescriptions are merely for convenience and that such actions in factresult from computing devices, processors, controllers, or other devicesexecuting the firmware, software, routines, instructions, etc.

In block diagrams, illustrated components are depicted as discretefunctional blocks, but embodiments are not limited to systems in whichthe functionality described herein is organized as illustrated. Thefunctionality provided by each of the components may be provided bysoftware or hardware modules that are differently organized than ispresently depicted, for example such software or hardware may beintermingled, conjoined, replicated, broken up, distributed (e.g. withina data center or geographically), or otherwise differently organized.The functionality described herein may be provided by one or moreprocessors of one or more computers executing code stored on a tangible,non-transitory, machine readable medium. In some cases, third partycontent delivery networks may host some or all of the informationconveyed over networks, in which case, to the extent information (e.g.,content) is said to be supplied or otherwise provided, the informationmay be provided by sending instructions to retrieve that informationfrom a content delivery network.

Unless specifically stated otherwise, as apparent from the discussion,it is appreciated that throughout this specification discussionsutilizing terms such as “processing,” “computing,” “calculating,”“determining” or the like refer to actions or processes of a specificapparatus, such as a special purpose computer or a similar specialpurpose electronic processing/computing device.

The reader should appreciate that the present application describesseveral inventions. Rather than separating those inventions intomultiple isolated patent applications, these inventions have beengrouped into a single document because their related subject matterlends itself to economies in the application process. But the distinctadvantages and aspects of such inventions should not be conflated. Insome cases, embodiments address all of the deficiencies noted herein,but it should be understood that the inventions are independentlyuseful, and some embodiments address only a subset of such problems oroffer other, unmentioned benefits that will be apparent to those ofskill in the art reviewing the present disclosure. Due to costsconstraints, some inventions disclosed herein may not be presentlyclaimed and may be claimed in later filings, such as continuationapplications or by amending the present claims. Similarly, due to spaceconstraints, neither the Abstract nor the Summary sections of thepresent document should be taken as containing a comprehensive listingof all such inventions or all aspects of such inventions.

It should be understood that the description and the drawings are notintended to limit the present disclosure to the particular formdisclosed, but to the contrary, the intention is to cover allmodifications, equivalents, and alternatives falling within the spiritand scope of the inventions as defined by the appended claims.

Modifications and alternative embodiments of various aspects of theinventions will be apparent to those skilled in the art in view of thisdescription. Accordingly, this description and the drawings are to beconstrued as illustrative only and are for the purpose of teaching thoseskilled in the art the general manner of carrying out the inventions. Itis to be understood that the forms of the inventions shown and describedherein are to be taken as examples of embodiments. Elements andmaterials may be substituted for those illustrated and described herein,parts and processes may be reversed or omitted, certain features may beutilized independently, and embodiments or features of embodiments maybe combined, all as would be apparent to one skilled in the art afterhaving the benefit of this description. Changes may be made in theelements described herein without departing from the spirit and scope ofthe invention as described in the following claims. Headings used hereinare for organizational purposes only and are not meant to be used tolimit the scope of the description.

As used throughout this application, the word “may” is used in apermissive sense (i.e., meaning having the potential to), rather thanthe mandatory sense (i.e., meaning must). The words “include”,“including”, and “includes” and the like mean including, but not limitedto. As used throughout this application, the singular forms “a,” “an,”and “the” include plural referents unless the content explicitlyindicates otherwise. Thus, for example, reference to “an” element or “a”element includes a combination of two or more elements, notwithstandinguse of other terms and phrases for one or more elements, such as “one ormore.” As used herein, unless specifically stated otherwise, the term“or” encompasses all possible combinations, except where infeasible. Forexample, if it is stated that a database can include A or B, then,unless specifically stated otherwise or infeasible, the database caninclude A, or B, or A and B. As a second example, if it is stated that adatabase can include A, B, or C, then, unless specifically statedotherwise or infeasible, the database can include A, or B, or C, or Aand B, or A and C, or B and C, or A and B and C. Terms describingconditional relationships, e.g., “in response to X, Y,” “upon X, Y,”,“if X, Y,” “when X, Y,” and the like, encompass causal relationships inwhich the antecedent is a necessary causal condition, the antecedent isa sufficient causal condition, or the antecedent is a contributorycausal condition of the consequent, e.g., “state X occurs upon conditionY obtaining” is generic to “X occurs solely upon Y” and “X occurs upon Yand Z.” Such conditional relationships are not limited to consequencesthat instantly follow the antecedent obtaining, as some consequences maybe delayed, and in conditional statements, antecedents are connected totheir consequents, e.g., the antecedent is relevant to the likelihood ofthe consequent occurring. Statements in which a plurality of attributesor functions are mapped to a plurality of objects (e.g., one or moreprocessors performing steps A, B, C, and D) encompasses both all suchattributes or functions being mapped to all such objects and subsets ofthe attributes or functions being mapped to subsets of the attributes orfunctions (e.g., both all processors each performing steps A-D, and acase in which processor 1 performs step A, processor 2 performs step Band part of step C, and processor 3 performs part of step C and step D),unless otherwise indicated. Further, unless otherwise indicated,statements that one value or action is “based on” another condition orvalue encompass both instances in which the condition or value is thesole factor and instances in which the condition or value is one factoramong a plurality of factors. Unless otherwise indicated, statementsthat “each” instance of some collection have some property should not beread to exclude cases where some otherwise identical or similar membersof a larger collection do not have the property, i.e., each does notnecessarily mean each and every. References to selection from a rangeincludes the end points of the range.

In the above description, any processes, descriptions or blocks inflowcharts should be understood as representing modules, segments orportions of code which include one or more executable instructions forimplementing specific logical functions or steps in the process, andalternate implementations are included within the scope of the exemplaryembodiments of the present advancements in which functions can beexecuted out of order from that shown or discussed, includingsubstantially concurrently or in reverse order, depending upon thefunctionality involved, as would be understood by those skilled in theart.

To the extent certain U.S. patents, U.S. patent applications, or othermaterials (e.g., articles) have been incorporated by reference, the textof such U.S. patents, U.S. patent applications, and other materials isonly incorporated by reference to the extent that no conflict existsbetween such material and the statements and drawings set forth herein.In the event of such conflict, any such conflicting text in suchincorporated by reference U.S. patents, U.S. patent applications, andother materials is specifically not incorporated by reference herein.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the present disclosures. Indeed, the novel methods, apparatusesand systems described herein can be embodied in a variety of otherforms; furthermore, various omissions, substitutions and changes in theform of the methods, apparatuses and systems described herein can bemade without departing from the spirit of the present disclosures. Theaccompanying claims and their equivalents are intended to cover suchforms or modifications as would fall within the scope and spirit of thepresent disclosures.

The invention claimed is:
 1. A method comprising: obtaining a spatialmap of a distribution of a residue corresponding to a characteristic ofa pattern on a substrate subjected to a patterning process; determining,by a hardware computing system, a zone of the spatial map based on avariation of the distribution of the residue within the spatial map; anddetermining, by the hardware computing system and based on the zone andthe distribution of the residue values or the values of thecharacteristic of the pattern on the substrate within the zone, aprobabilistic model configured to predict the characteristic.
 2. Themethod of claim 1, wherein the determining the zone comprises:determining that the variation of the distribution of the residueexceeds a certain threshold; and responsive to the variation of thedistribution of the residue exceeding the threshold, defining adifferent zone.
 3. The method of claim 1, wherein the determining thezone is an iterative process, wherein a plurality of zones are obtainedbased on the variation of the distribution of the residue, such that afirst zone of the plurality of zones has a first variation of thedistribution of the residue, and a second zone of the plurality of zoneshas a second variation of the distribution of the residue.
 4. The methodof claim 3, wherein an iteration of the determining the zone comprises:executing a classification algorithm with the spatial map of thedistribution of the residue as input, the classification algorithmproviding one or more groups of the residue based on the variation inresidue; and identifying a boundary around each group of the one or moregroups of residue, wherein the zone is a region within the boundary. 5.The method of claim 4, wherein the classification algorithm is a machinelearning model trained to identify zones based on the variation of thedistribution of the residue or the variation of the characteristic ofthe pattern on the substrate.
 6. The method of claim 4, wherein theclassification algorithm involves a clustering analysis based on atleast one selected from: k-nearest mean; mean-shifting; naive-Bayes andback propagation neural network; Density-Based Spatial Clustering ofApplications with Noise; Gaussian mixture model; or hierarchicalclustering.
 7. The method of claim 3, wherein the iteration of thedetermining the zone further comprises: obtaining, via a metrology tool,metrology data in the first zone and the second zone corresponding tothe characteristic of the pattern on the substrate, wherein the firstzone and the second zone are separated by a first boundary between thefirst zone and the second zone, and the second zone is identified by asecond boundary; and modifying the first boundary around the first zoneof the residue based on the metrology data.
 8. The method of claim 1,wherein the determining the zone comprises determining a radial boundaryand an angular span of the radial boundary based on the variation of thedistribution of the residue exceeding a certain threshold in the radialdirection, an angular direction or both.
 9. The method of claim 1,wherein the zone is defined in terms of radial distance from a center ofthe substrate.
 10. The method of claim 1, wherein the zone comprises anirregular closed boundary in a radial direction and spanning a certainangular region of the substrate.
 11. The method of claim 1, wherein thedetermining the probabilistic model comprises: obtaining values of thecharacteristic of the pattern on the substrate within the zone; anddetermining statistical parameters of the probabilistic model based onvalues of the characteristic of the pattern or values of the residuecorresponding to the characteristic of the pattern within the zone. 12.The method of claim 11, wherein the statistical parameters of theprobabilistic model comprise a mean value and a standard deviationvalue.
 13. The method of claim 11, wherein the probabilistic model is aGaussian distribution.
 14. The method of claim 1, further comprising:obtaining, via a metrology tool, additional metrology data correspondingto subsequently processed substrates and distribution of the residuescorresponding to the additional data; adjusting, via the computingsystem, the zone based on the distribution of the residues correspondingto the additional data; and adjusting, via the computing system, theprobabilistic model based on the adjusted zone.
 15. A computer programproduct comprising a non-transitory computer readable medium havinginstructions therein, the instructions, upon execution by a computersystem, configured to cause the computer system to at least: obtain aspatial map of a distribution of a residue corresponding to acharacteristic of a pattern on a substrate subjected to a patterningprocess; determine a zone of the spatial map based on a variation of thedistribution of the residue within the spatial map; and determine, basedon the zone and the distribution of the residue values or the values ofthe characteristic of the pattern on the substrate within the zone, aprobabilistic model configured to predict the characteristic.
 16. Thecomputer program product of claim 15, wherein the instructionsconfigured to cause the computer system to determine the zone arefurther configured to cause the computer system to: determine that thevariation of the distribution of the residue exceeds a certainthreshold; and responsive to the variation of the distribution of theresidue exceeding the threshold, define a different zone.
 17. Thecomputer program product of claim 15, wherein the instructionsconfigured to cause the computer system to determine the zone arefurther configured to cause the computer system to determine the zone inan iterative process, wherein a plurality of zones are obtained based onthe variation of the distribution of the residue, such that a first zoneof the plurality of zones has a first variation of the distribution ofthe residue, and a second zone of the plurality of zones has a secondvariation of the distribution of the residue.
 18. The computer programproduct of claim 17, wherein the instructions configured to cause thecomputer system to determine the zone are further configured to causethe computer system to, for an iteration of the determination of thezone: execute a classification algorithm with the spatial map of thedistribution of the residue as input, the classification algorithmproviding one or more groups of the residue based on the variation inresidue; and identify a boundary around each group of the one or moregroups of residue, wherein the zone is a region within the boundary. 19.The computer program product of claim 17, wherein the instructionsconfigured to cause the computer system to determine the zone arefurther configured to cause the computer system to, for an iteration ofthe determination of the zone: obtain metrology data, determined by ametrology tool, in the first zone and the second zone corresponding tothe characteristic of the pattern on the substrate, wherein the firstzone and the second zone are separated by a first boundary between thefirst zone and the second zone, and the second zone is identified by asecond boundary; and modify the first boundary around the first zone ofthe residue based on the metrology data.
 20. The computer programproduct of claim 15, wherein the instructions configured to cause thecomputer system to determine the zone are further configured to causethe computer system to determine a radial boundary and an angular spanof the radial boundary based on the variation of the distribution of theresidue exceeding a certain threshold in the radial direction, anangular direction or both.